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Tabular Integrals

$$\int\frac{dx}{x}=\ln|x|$$

$$\int x^n dx=\frac{x^n}{n+1}$$

$$\int a^x dx=\frac{a^x}{\ln{a}}$$

$$\int e^x dx=e^x$$

$$\int\cos{x}dx=-\sin{x}$$

$$\int \sin{x}dx=-\cos{x}$$

$$\int \frac{dx}{\cos^2{x}}=\tan{x}$$

$$\int\frac{dx}{\sin^2{x}}=-\cot{x}$$

$$\int\frac{dx}{x^2+a^2}=\frac{1}{a}\arctan{\frac{x}{a}}$$

$$\int\frac{dx}{a^2-x^2}=\frac{1}{2a}\ln\Big|\frac{x+a}{a-x}\Big|$$

$$\int\frac{dx}{\sqrt{a^2-x^2}}=\arcsin{\frac{x}{a}}$$

$$\int\frac{dx}{\sqrt{x^2\pm a^2}}=\ln\big|x\pm \sqrt{x^2\pm a^2}\big|$$

1

$$\int (2-3\sqrt{x})^2dx$$

$$4x-8x^{3/2}+\frac{9}{2}x^2$$
2

$$\int \frac{\sqrt{x}+\sqrt[3]{x}}{\sqrt[4]{x}} dx$$

$$\frac{4x^{\frac{5}{4}}}{5}+\frac{12x^{\frac{13}{12}}}{13}$$
3

$$\int \Big(\frac{1+x}{x}\Big)^2dx$$

$$x+2\ln|x|-\frac{1}{x}$$
4

$$\int \Big(\frac{1}{x}+\frac{2}{x^2}+\frac{3}{x^3}\Big)dx$$

$$\ln|x|-\frac{2}{x}-\frac{3}{2x^2}$$
5

$$\int \frac{(1+x)^3}{x^2}dx$$

$$\frac{x^2}{2}+3x+3\ln|x|-\frac{1}{x}$$
6

$$\int \frac{x^2}{1-x^2}dx$$

$$-x+\frac{1}{2}\ln|\frac{x+1}|$$
7

$$\int \frac{4-x^2}{3+x^2}dx$$

$$\frac{7}{\sqrt3}\arctan{\frac{x}{\sqrt3}}-x$$
8

$$\int \frac{dx}{(x^2+1)(x^2-3)}$$

$$\frac{1}{8\sqrt3}\ln|\frac{x-\sqrt3}{x+\sqrt3}| -\frac{\arctan{x}}{4}$$
9

$$\int \frac{dx}{x^4-1}$$

$$\frac{1}{4}\ln|\frac{x-1}{x+1}|-\frac{\arctan{x}}{2}$$
10

$$\int \frac{1+2x^2}{x^2(1+x^2)}dx$$

$$-\frac{1}{x}+\arctan{x}$$
11

$$\int\frac{(1+x)^2}{x(1+x^2)}dx$$

$$\ln|x|+2\arctan{x}$$
12

$$\int\frac{\sqrt{1+x^2}+\sqrt{1-x^2}}{\sqrt{1-x^4}}dx$$

$$\arcsin{x}+\ln|x+\sqrt{x^2+1}|$$
13

$$\int\frac{\sqrt{x^2+1}-\sqrt{x^2-1}}{\sqrt{x^4-1}}dx$$

$$\ln\Big|\frac{x+\sqrt{x^2-1}}{x+\sqrt{x^2+1}}\Big|$$
14

$$\int\frac{dx}{2x^2+3}$$

$$\frac{1}{\sqrt6}\arctan{(\frac{\sqrt2x}{\sqrt3})}$$
15

$$\int\frac{dx}{3x^2-7}$$

$$\frac{1}{2\sqrt21}\ln\Big|\frac{\sqrt3x-\sqrt7}{\sqrt3x+\sqrt7}\Big|$$
16

$$\int\frac{dx}{\sqrt{2-x^2}}$$

$$\arcsin\frac{x}{\sqrt2}$$
17

$$\int\frac{dx}{\sqrt{2x^2+5}}$$

$$\frac{1}{\sqrt2}\ln|\sqrt2x+\sqrt{2x^2+5}|$$
18

$$\int\frac{dx}{\sqrt{3x^2-7}}$$

$$\frac{1}{\sqrt3}\ln|\sqrt3x+\sqrt{3x^2-7}|$$
19

$$\int(5^x-2^x)^2dx$$

$$\frac{25^x}{\ln25}+\frac{4^x}{\ln4}-\frac{2\times 10^x}{\ln10}$$
20

$$\int\Big(\frac{2^{2x-1}-3^{2x+3}}{6^{2x}}\Big)dx$$

$$-\frac{1}{2\ln9}\times\Big(\frac{1}{9}\Big)^x+\frac{27}{\ln4}\times\Big(\frac{1}{4}\Big)^x$$
21

$$\int 2^x3^x5^xdx$$

$$\frac{30^x}{\ln30}$$
22

$$\int \frac{2^x3^{2x}4^{3x}}{5^x6^{2x}}dx$$

$$\frac{\Big(\frac{32}{5}\Big)^x}{\ln\frac{32}{5}}$$
23

$$\int\frac{e^{3x}-1}{e^x-1}dx$$

$$\frac{e^{2x}}{2}+e^x+x$$
24

$$\int\frac{2^{2x}-1}{\sqrt{2^x}}dx$$

$$\frac{2}{\ln2}\Big(\frac{2^{\frac{3x}{2}}}{3}+2^{\frac{-x}{2}}\Big)$$
25

$$\int \sin^2{\frac{x}{2}}dx$$

$$\frac{x}{2}-\frac{\sin{x}}{2}$$
26

$$\int \cos^2{\frac{x}{2}}dx$$

$$\frac{x}{2}+\frac{\sin{x}}{2}$$
27

$$\int\frac{dx}{\sin^2{x}\cos^2{x}}$$

$$\tan{x}-\cot{x}$$
28

$$\int\frac{\cos{2x}}{\sin^2{2x}}dx$$

$$-\frac{1}{4}(\cot{x}+\tan{x})$$
29

$$\int\cot^2{x}dx$$

$$-\cot{x}-x$$
30

$$\int\tan^2{x}dx$$

$$\tan{x}-x$$
31

$$\int\frac{dx}{x-1}$$

$$\ln|x-1|$$
32

$$\int\frac{dx}{2x+3}$$

$$\frac{1}{2}\ln|2x+3|$$
33

$$\int\frac{dx}{(x+2)(x+3)}$$

$$\ln\Big|\frac{x+2}{x+3}\Big|$$
34

$$\int\frac{x+3}{(x+2)(x-1)}dx$$

$$\frac{1}{3}\ln\Big|\frac{(x-1)^4)}{x+2}\Big|$$
35

$$\int\frac{2+x}{1+x}dx$$

$$x+\ln|1+x|$$
36

$$\int\frac{xdx}{1+2x}$$

$$\frac{1}{2}x-\frac{1}{4}\ln|2x+1|$$
37

$$\int(x-1)^{10}dx$$

$$\frac{(x-1)^{11}}{11}$$
38

$$\int(2x+5)^{17}dx$$

$$\frac{(2x+5)^{18}}{36}$$
39

$$\int\frac{dx}{(1-3x)^{30}}$$

$$\frac{1}{87}\frac{1}{(1-3x)^{29}}$$
40

$$\int\frac{dx}{\sqrt{1-2x}}$$

$$-\sqrt{1-2x}$$
41

$$\int\frac{dx}{\sqrt[5]{(1+3x)^4}}$$

$$\frac{5}{3}\sqrt[5]{1+3x}$$
42

$$\int\sqrt[15]{1+4x}dx$$

$$\frac{15}{64}(1+4x)^{\frac{16}{15}}$$
43

$$\int x(x-2)^5dx$$

$$\frac{(x-2)^7}{7}+\frac{1}{3}(x-2)^6$$
44

$$\int x\sqrt{1-2x}dx$$

$$\frac{(1-2x)^{\frac{5}{2}}}{10}-\frac{(1-2x)^{\frac{3}{2}}}{6}$$
45

$$\int (x+2)(\sqrt{x-2})dx$$

$$\frac{2}{5}(x-2)^{\frac{5}{2}}+\frac{8}{3}(x-2)^{\frac{3}{2}}$$
46

$$\int\frac{2x-7}{\sqrt{1+3x}}dx$$

$$\frac{4}{27}(1+3x)^{\frac{3}{2}})-\frac{46}{9}\sqrt{1+3x}$$
47

$$\int\frac{x^2+1}{x+1}dx$$

$$\frac{x^2}{2}-x+2\ln|x+1|$$
48

$$\int\frac{x^2+1}{2x-1}dx$$

$$\frac{x^2}{4}+\frac{x}{4}+\frac{5}{8}\ln|2x-1|$$
49

$$\int(2x+3)^2(1-x)^8dx$$

$$-\frac{4}{11}(1-x)^{11}+2(1-x)^{10}-\frac{25}{9}(1-x)^9$$
50

$$\int\frac{x-4}{\sqrt{x^2-2}}dx$$

$$\sqrt{x^2-2}-4\ln|x+\sqrt{x^2-2}|$$
51

$$\int\frac{x^3dx}{x^2-4}$$

$$\frac{1}{2}x^2+2\ln|x^2-4|$$
52

$$\int\frac{xdx}{\sqrt{1-x^4}}$$

$$\frac{1}{2}\arcsin{x^2}$$
53

$$\int\frac{x+2}{\sqrt{x^2-10}}dx$$

$$\sqrt{x^2-10}+2ln|x+\sqrt{x^2-10}|$$
54

$$\int\frac{1-4x}{\sqrt{1-2x^2}}dx$$

$$\frac{1}{\sqrt2}\arcsin{\sqrt2x}+2\sqrt{1-2x^2}$$
55

$$\int x\sqrt{1-x^2}dx$$

$$-\frac{(1-x^2)^{\frac{3}{2}}}{3}$$
56

$$\int x(1-x^2)^5dx$$

$$-\frac{(1-x^2)^6}{12}$$
57

$$\int \frac{xdx}{1+x^4}$$

$$\frac{1}{2}\arctan{x^2}$$
58

$$\int\frac{x^2dx}{x^6-5}$$

$$\frac{1}{6\sqrt5}\ln\Big|\frac{x^3-\sqrt5}{x^3+\sqrt5}\Big|$$
59

$$\int\frac{x^4dx}{\sqrt{3+x^5}}$$

$$\frac{2}{5}\sqrt{3+x^5}$$
60

$$\int\frac{dx}{x\ln^5x}$$

$$-\frac{1}{4\ln^4x}$$
61

$$\int \frac{dx}{x\sqrt{\ln{x}}}$$

$$2\sqrt{\ln{x}}$$
62

$$\int\frac{dx}{x(\ln{x}+3)}$$

$$\ln|\ln{x}+3|$$
63

$$\int\frac{dx}{x(2+\ln^2x)}$$

$$\frac{1}{\sqrt2}\arctan{\frac{\ln{x}}{\sqrt2}}$$
64

$$\int\frac{\sqrt[3]{\ln^2x}dx}{x}$$

$$\frac{3}{5}\ln^{\frac{5}{3}}x$$
65

$$\int\frac{e^x+e^{2x}}{1-e^x}dx$$

$$-e^x-2\ln|e^x-1|$$
66

$$\int\frac{e^x}{1+e^x}dx$$

$$\ln|1+e^x|$$
67

$$\int \sin{5x}dx$$

$$-\frac{1}{5}\cos{5x}$$
68

$$\int\cos{\frac{x}{7}}dx$$

$$7\sin{\frac{x}{7}}$$
69

$$\int \frac{\sin{x}\cos{x}}{\sqrt{a^2\sin^2{x}+b^2\cos^2{x}}}dx$$

$$\frac{\sqrt{a^2\sin^2{x}+b^2\cos^2{x}}}{a^2-b^2}, a^2 \neq b^2$$
70

$$\int \cos{\alpha x}\sin{\beta x}dx$$

$$-\frac{\cos{(\alpha-\beta)x}}{2(\alpha-\beta)}-\frac{\cos{(\alpha+\beta)x}}{2(\alpha+\beta)}$$
71

$$\int \cos{\alpha x}\cos{\beta x}dx$$

$$\frac{\sin{(\alpha-\beta)x}}{2(\alpha-\beta)}+\frac{\sin{(\alpha+\beta)x}}{2(\alpha+\beta)}$$
72

$$\int \sin{\alpha x}\sin{\beta x}dx$$

$$\frac{\sin{(\alpha-\beta)x}}{2(\alpha-\beta)}-\frac{\sin{(\alpha+\beta)x}}{2(\alpha+\beta)}$$
73

$$\int \sin^2{x}\cos{\alpha x}dx$$

$$\frac{\sin{\alpha x}}{2\alpha}-\frac{\sin{(\alpha-2)x}}{4(\alpha-2)}-\frac{\sin{(\alpha+2)x}}{4(\alpha+2)}$$
74

$$\int \cos^3{x}\sin{\beta x} dx$$

$$-\frac{3}{8}\Big[\frac{\cos{(\beta-1)x}}{(\beta-1)x}+\frac{\cos{(\beta+1)x}}{(\beta+1)x}\Big]-\frac{1}{8}\Big[\frac{\cos{(\beta-3)x}}{(\beta-3)}+\frac{\cos{(\beta+3)x}}{(\beta+3)}\Big]$$
75

$$\int x\sin{x^2}dx$$

$$-\frac{1}{2}\cos{x^2}$$
76

$$\int\frac{\cos{\sqrt{x}dx}}{\sqrt{x}}$$

$$2\sin{\sqrt{x}}$$
77

$$\int\frac{\cos{x}dx}{1+\sin{x}}$$

$$\ln|\sin{x}+1|$$
78

$$\int\sin^2{x}dx$$

$$\frac{x}{2}-\frac{1}{4}\sin{2x}$$
79

$$\int\cos^2{x}dx$$

$$\frac{x}{2}+\frac{1}{4}\sin{2x}$$
80

$$\int(\sin{x}+2\cos{x})^2dx$$

$$\frac{5}{2}x+\frac{3}{4}\sin{2x}-\cos{2x}$$
81

$$\int e^x\cos{e^x}dx$$

$$\sin{e^x}$$
82

$$\int\frac{\cos{x}dx}{1+\cos^2{x}}$$

$$\frac{1}{2\sqrt2}\ln|\frac{\sin{x}+\sqrt2}{\sin{x}-\sqrt2}|$$
83

$$\int\frac{dx}{\sin^2{7x}}$$

$$-\frac{\cot{7x}}{7}$$
84

$$\int\frac{dx}{\cos^2{8x}}$$

$$\frac{\tan{8x}}{8}$$
85

$$\int\frac{dx}{\sin{3x}}$$

$$\frac{1}{3}\ln|\tan{\frac{3x}{2}}|$$
86

$$\int\frac{dx}{\cos{x}}$$

$$\ln|\tan{(\frac{x}{2}}+\frac{\pi}{4})|$$
87

$$\int\tan{x}dx$$

$$-\ln|\cos{x}|$$
88

$$\int\cot{x}dx$$

$$\ln|\sin{x}|$$
89

$$\int\frac{dx}{1+\cos{x}}$$

$$\tan{\frac{x}{2}}$$
90

$$\int\frac{dx}{\sin{x}+\cos{x}}$$

$$\frac{1}{\sqrt2}\ln|\tan{(\frac{x}{2}+\frac{\pi}{8})}$$
91

$$\int\frac{1+\cos{x}}{(x+\sin{x})^3}dx$$

$$-\frac{1}{2(x+\sin{x})^2}$$
92

$$\int\frac{\sin{2x}}{\sqrt{1-4\sin^2{x}}}dx$$

$$-\frac{1}{2}\sqrt{1-4\sin^2{x}}$$
93

$$\int\frac{\sin{x}dx}{\sqrt{2-\sin^2{x}}}$$

$$-\ln|\cos{x}+\sqrt{1+\cos^2{x}}|$$
94

$$\int\frac{1}{\cos^2{x}}\frac{dx}{(1+\tan{x})}$$

$$\ln|\tan{x}+1|$$
95

$$\int\frac{1}{\sin^2{x}}\frac{dx}{(1+\tan{x})}$$

$$-\cot{x}+\ln|cot{x}+1|$$
96

$$\int\frac{\sin{x}\cos{x}}{\sqrt{3-\sin^4x}}dx$$

$$\frac{1}{2}\arcsin{\Big(\frac{\sin^2{x}}{\sqrt3}\Big)}$$
97

$$\int\frac{\textrm{arccot}3xdx}{1+9x^2}$$

$$-\frac{1}{6}\textrm{arccot}^2{3x}$$
98

$$\int\frac{(x+\sqrt{\arctan{2x}})}{1+4x^2}dx$$

$$\frac{1}{8}\ln|1+4x^2|+\frac{1}{3}\sqrt{(\arctan{2x})^3}$$
99

$$\int\frac{(\arcsin{x}-\arccos{x})}{\sqrt{1-x^2}}dx$$

$$\frac{\arcsin^2{x}+\arccos^2{x}}{2}$$
100

$$\int\frac{(x+\arcsin^3{2x})}{\sqrt{1-4x^2}}dx$$

$$-\frac{1}{4}\sqrt{1-4x^2}+\frac{1}{8}\arcsin^4{2x}$$
101

$$\int\frac{(x+\arccos^{\frac{3}{2}}{x})}{\sqrt{1-x^2}}dx$$

$$-\frac{2}{5}\arccos^{\frac{5}{2}}{x}$$
102

$$\int x^2\sqrt{a^2+x^2}dx$$

$$-\frac{a^2}{8}x\sqrt{a^2+x^2}+\frac{x(a^2+x^2)^{\frac{3}{2}}}{4}-\frac{a^4}{8}\ln|x+\sqrt{a^2+x^2}|$$
103

$$\int x^2\sqrt{a^2-x^2}dx$$

$$\frac{a^4}{8}\arcsin{x}\,-\,\frac{x(a^2-x^2)^{\frac{3}{2}}}{4}+\frac{a^2x\sqrt{a^2-x^2}}{8}$$
104

$$\int x^2\sqrt{x^2-a^2}dx$$

$$\frac{x(x^2-a^2)^{\frac{3}{2}}}{4}+\frac{a^2}{8}x\sqrt{x^2-a^2}-\frac{a^4}{8}\ln|x+\sqrt{x^2-a^2}|$$
105

$$\int\frac{x^2}{(a^2-x^2)^{\frac{3}{2}}}dx$$

$$\frac{x}{\sqrt{a^2-x^2}}-\arcsin{\frac{x}{a}}$$
106

$$\int\frac{x^4}{(a^2+x^2)^2}dx$$

$$x+\frac{a^2x}{2(a^2+x^2)}-\frac{3}{2}\arcsin{\frac{x}{a}}$$
107

$$\int\frac{dx}{(a^2+x^2)^{\frac{3}{2}}}$$

$$\frac{x}{a^2\sqrt{x^2+a^2}}$$
108

$$\int\sqrt{a^2-x^2}\,dx$$

$$\frac{x}{2}\sqrt{a^2-x^2}+\frac{a^2}{2}\arcsin{\frac{x}{a}}$$
109

$$\int\sqrt{x^2 \pm a^2}\,dx$$

$$\frac{x}{2}\sqrt{x^2\pm a^2}\,\,\pm\frac{a^2}{2}\ln|x+\sqrt{x^2\pm a^2}|$$
110

$$\int\frac{dx}{\sqrt{y}},\,y=ax^2+bx+c, a \neq 0$$

$$\frac{1}{\sqrt{a}}\ln|\frac{y'}{2}+\sqrt{ay}|, a>0; \frac{1}{\sqrt{-a}}\arcsin{\Big(\frac{-y'}{\sqrt{b^2-4ac}}\Big)}, a<0$$
111

$$\int\frac{xdx}{\sqrt{5+x-x^2}}$$

$$-\sqrt{5+x-x^2}+\frac{1}{2}\arcsin{\frac{2x-1}{\sqrt{21}}}$$
112

$$\int\frac{x+1}{\sqrt{x^2+x+1}}d$$

$$\frac{1}{2}\ln{\Big(\frac{2x+1}{2}+\sqrt{x^2+x+1}\Big)}+\sqrt{x^2+x+1}$$
113

$$\int\frac{xdx}{\sqrt{1-3x^2-2x^4}}$$

$$\frac{1}{2\sqrt{2}}\arcsin{\frac{4x^2+3}{\sqrt{17}}}$$
114

$$\int\frac{\cos{x}dx}{\sqrt{1+\sin{x}+\cos^2{x}}}$$

$$\arcsin{\frac{2\sin{x}-1}{3}}$$
115

$$\int\frac{x^3dx}{\sqrt{x^4-2x^2-1}}$$

$$\frac{1}{2}\ln{|x^2-1+\sqrt{x^4-2x^2-1}|}+\frac{1}{2}\sqrt{x^4-2x^2-1}$$
116

$$\int\frac{x+x^3}{\sqrt{1+x^2-x^4}}dx$$

$$-\frac{1}{2}\sqrt{1+x^2-x^4}+\frac{3}{4}\arcsin{\frac{2x^2-1}{\sqrt{5}}}$$
117

$$\int\frac{dx}{x\sqrt{x^2+x+1}}$$

$$-\ln\Big|\frac{x+2+2\sqrt{x^2+x+1}}{x}\Big|$$
118

$$\frac{dx}{x^2\sqrt{x^2+x-1}}$$

$$\frac{\sqrt{x^2+x-1}}{x}+\frac{1}{2}\arcsin{\frac{x-2}{x\sqrt{5}}}$$
119

$$\int\frac{dx}{(x+1)\sqrt{x^2+1}}$$

$$-\frac{1}{\sqrt{2}}\ln{\Big|\frac{1-x+\sqrt{2(1+x^2)}}{x+1}\Big|}$$
120

$$\int\frac{dx}{(x-1)\sqrt{x^2-2}}$$

$$\arcsin{\frac{x-2}{(x-1)\sqrt{2}}}$$
121

$$\int\frac{dx}{(x+2)^2\sqrt{x^2+2x-5}}$$

$$\frac{1}{5}\frac{\sqrt{x^2+2x-5}}{x+2}+\frac{1}{5\sqrt{5}}\arcsin{\frac{x+7}{(x+2)\sqrt{6}}}$$
122

$$\int\sqrt{2+x-x^2}dx$$

$$\frac{2x-1}{4}\sqrt{2+x-x^2}+\frac{9}{8}\arcsin{\frac{2x-1}{3}}$$
123

$$\int\sqrt{2+x+x^2}dx$$

$$\frac{7}{8}\ln{\Big(1+2x+2\sqrt{2+x+x^2}\Big)}+\frac{2x+1}{4}\sqrt{2+x+x^2}$$
124

$$\int\sqrt{x^4+2x^2-1}dx$$

$$\frac{x^2+1}{4}\sqrt{x^4+2x^2-1}-\frac{1}{2}\ln{|x^2+1+\sqrt{x^4+2x^2-1}|}$$
125

$$\int\frac{1-x+x^2}{x\sqrt{1+x-x^2}}dx$$

$$-\sqrt{1+x-x^2}-\frac{1}{2}\arcsin{\frac{2x-1}{\sqrt{5}}}-\ln{\Big|\frac{2+x+2\sqrt{1+x-x^2}}{x}\Big|}$$
126

$$\int\frac{x^2+1}{x\sqrt{x^4+1}}dx$$

$$\ln{\Big|\frac{x^2-1+\sqrt{x^4+1}}{x}\Big|}$$
127

$$\int\sqrt{e^{3x}+e^{2x}}dx$$

$$\frac{2}{3}(1+e^x)^{\frac{3}{2}}$$
128

$$\int\frac{dx}{\sqrt{e^x+1}}$$

$$\ln\Big|\frac{\sqrt{e^x+1}-1}{\sqrt{e^x+1}+1}\Big|$$
129

$$\int\frac{\sqrt[3]{1+\sqrt[4]{x}}}{\sqrt{x}}dx$$

$$\frac{12}{7}(1+\sqrt[4]{x})^{\frac{7}{3}}-3(1+\sqrt[4]{x})^{\frac{4}{3}}$$
130

$$\int\frac{dx}{x\sqrt[4]{1+x^7}}$$

$$\frac{2}{7}\arctan{\sqrt[4]{1+x^7}}+\frac{1}{7}\ln\Big|\frac{\sqrt[4]{1+x^7}-1}{\sqrt[4]{1+x^7}+1}\Big|$$
131

$$\int\frac{dx}{\sqrt{x}(1+\sqrt[3]{x})}$$

$$6\sqrt[6]{x}-6\arctan{\sqrt[6]{x}}$$
132

$$\int\frac{dx}{x^2(2+x^3)^{\frac{5}{3}}}$$

$$-\frac{1}{8}\,\,\frac{4+3x^3}{x(2+x^3)^{\frac{2}{3}}}$$
133

$$\int 5^{\sqrt{x}}dx$$

$$\Big(\frac{2}{\ln^25}\Big)\,5^{\sqrt{x}}(\ln5\,\sqrt{x}-1)$$
134

$$\int x\cos{\sqrt{x}}dx$$

$$6(x-2)\cos{\sqrt{x}}\,+\,2\sqrt{x}\,\,(x-6)\sin{\sqrt{x}}$$