1
$$\int\frac{1+\cos{x}}{x+\sin{x}}dx$$
2
$$\int_0^{\sqrt3}\frac{\arctan{x}+\text{arccot}\,x}{x}dx$$
3
$$\int_0^{2022}\big(x^2-\left\lfloor x \right\rfloor \left\lceil x \right\rceil\big) dx$$
4
$$\int\frac{\sinh{x}}{\cosh{x}-\sinh{x}}dx$$
5
$$\int\frac{x}{\sqrt{x-1}+\sqrt{x+1}}dx$$
6
$$\int_0^{\pi}\cos{(x+\cos{x})}dx$$
7
$$\int x^3\sin{(x^2)}dx$$
8
$$\int\frac{x}{1-x^4}dx$$
9
$$\int\frac{dx}{\cosh^2{x}}$$
10
$$\int_0^1\big(e^{e^x}-e^{e^x-x}\big)dx$$
11
$$\lim_{n\to\infty}\int_0^3\underbrace{\sin\Big(\frac{\pi}{3}\sin\Big(\frac{\pi}{3}\sin\Big(\dots\sin{\Big(\frac{\pi}{3}x\Big)}\Big)\Big)\Big)}_{n\sin(\dots)}dx$$
12
$$\int_0^1\sqrt{1-\sqrt{x}}dx$$
13
$$\int\frac{x^3}{1+x+\frac{x^2}{2}+\frac{x^3}{6}}dx$$
14
$$\int \big[\sin(x+\sin{x})-\sin{(x-\sin{x})}\big]dx$$
15
$$\int\big(\tan^4{x}\sec^3{x}+\tan^2{x}\sec^5{x}\big)dx$$
16
$$\int(1+\ln{x})\ln{(\ln{x})}dx$$
17
$$\int\biggl(\frac{1}{1+\sin{x}}+\frac{1}{1+\cos{x}}+\frac{1}{1+\tan{x}}+\frac{1}{1+\cot{x}}+\frac{1}{1+\sec{x}}+\frac{1}{1+\csc{x}}\biggl)dx$$
18
$$\int\frac{dx}{\sqrt{x-x^2}}$$
19
$$\int_0^{\frac{1}{2}}\sum_{n=0}^{\infty}\binom{n+3}{n}x^ndx$$
20
$$\int\frac{dx}{1+\cos^2{x}}$$
1
$$\int\frac{\ln{2x}}{x\ln{x}}dx$$
2
$$\int_0^{\infty}\frac{dx}{e^x+1}$$
3
$$\int_e^{e^e}\frac{\ln{x}\cdot \ln{(\ln{x})}}{x}dx$$
4
$$\int_0^1\ln{\biggl(\frac{1+x}{1-x}\biggl)}dx$$
5
$$\int\frac{1}{x^2+(x-1)^2}dx$$
6
$$\int\sqrt{x\sqrt{x\sqrt{x\dots}}}dx$$
7
$$\int\sin^4{x}\cos^4{x}(\cos{x}+\sin{x})(\cos{x}-\sin{x})dx$$
8
$$\int\ln{(x^2+1)}dx$$
9
$$\int_0^{2\pi}\cos^{2020}{(x)}dx$$
10
$$\int\frac{2x+1}{2x^2+2x+1}dx$$
11
$$\int_{\frac{1}{\sqrt2}}^1\frac{\arcsin{x}}{x^3}dx$$
12
$$\int_0^{\frac{\pi}{2}}\sin{2x}\cos(\cos{x})dx$$
13
$$\int_0^{2\pi}\sin{(\sin{x}-x)}dx$$
14
$$\int\biggl(\frac{1}{x-1}+\frac{\sum_{k=0}^{2018}(k+1)x^k}{\sum_{k=0}^{2019}x^k}\biggl)dx$$
15
$$\int_0^{\frac{\pi}{2}}\frac{dx}{\tan^{\sqrt{2020}}{x}+1}$$
16
$$\int x(1-x)^{2020}dx$$
17
$$\int\frac{\sec^4{x}\tan{x}}{\sec^4{x}+4}dx$$
18
$$\int x^{2x}(2\ln{x}+2)dx$$
19
$$\int_0^1\sqrt{1-x^2}dx$$
20
$$\int_0^{\infty}x^5e^{-x^4}dx$$
1
$$\int_0^{2\pi}\tan{(\cos{x})dx}$$
2
$$\int\frac{x+1}{x(x+\ln{x})}dx$$
3
$$\int\big(e^{x+e^x}+e^{x-e^{-x}}\big)dx$$
4
$$\int_{-\frac{1}{2}}^{\frac{1}{2}}\frac{dx}{1-x^2}$$
5
$$\int_0^22^{\ln{x}}dx$$
6
$$\int_{-2\pi}^{2\pi}(\cos{3x}+\sin{2x})(-\sin{2019x}+\cos{3x})dx$$
7
$$\int\cos{x}\cdot\cos(\sin{x})\cdot\cos{(\sin{(\sin{x})})}dx$$
8
$$\int_0^{\infty}\frac{e^{-\frac{2019}{4t^2}}}{t^2}dt$$
9
$$\int\sin{(\sqrt{x})}dx$$
10
$$\int_0^1\frac{\sqrt{x}}{1+x}dx$$
11
$$\int_0^{2\pi}\cos{(x)}\cos{(2x)}\cos{(3x)}dx$$
12
$$\lim_{n\to\infty}\int_{-\infty}^{\infty}e^{-x^{2n}}dx$$
13
$$\int_0^ex^{\frac{1}{\ln{x}}}dx$$
14
$$\int_0^{\frac{\pi}{100}}\frac{\sin{(20x)}+\sin{(19x)}}{\cos{(20x)}+\cos{(19x)}}dx$$
15
$$\int (e^x\cos^2{x}+e^x\cos{x}\sin{x}-e^x\sin^2{x})dx$$
16
$$\int_0^{\frac{\pi}{2}}\frac{\sin{x}}{\sin{(x+\frac{\pi}{4})}}dx$$
17
$$\int\frac{dx}{x+\sqrt[3]{x}}$$
18
$$\int_0^2x^{x^2+1}(2\ln{x}+1)dx$$
19
$$\int\frac{2x^3-1}{x(x^3+1)}dx$$
20
$$\int\cos{(\arctan{x})}dx$$
1
$$\int\frac{e^x}{e^x+2}dx$$
2
$$\int\sqrt{x\sqrt[3]{x\sqrt[4]{x\sqrt[5]{x\dots}}}}dx$$
3
$$\int_0^{2018\pi}\big|\sin{(2018x)}\big|dx$$
4
$$\int\frac{dx}{\tan{x}+\cot{x}}$$
5
$$\int\frac{x^5}{2+x^{12}}dx$$
6
$$\int(\cos{x\cosh{x}+\sin{x}\sinh{x}})dx$$
7
$$\int\frac{e^x+\cos{x}}{e^x+\sin{x}}dx$$
8
$$\int\sin{\big[\cos{(\sin{x})}\big]}\sin{(\sin{x})}\cos{x}dx$$
9
$$\int\frac{dx}{1+\sin{x}}$$
10
$$\int\frac{\cos{x}}{1-\cos{2x}}dx$$
11
$$\int e^x\Big(\frac{1}{x}+\ln{x}\Big)dx$$
12
$$\int\tanh^2{x}dx$$
13
$$\int\frac{2017x^{2016}+2018x^{2017}}{1+x^{4034}+2x^{4035}+x^{4036}}dx$$
14
$$\int\frac{\sin{2x}-\sin^2{x}}{\cos{2x}-\cos^2{x}}dx$$
15
$$\int\frac{dx}{x^{\frac{25}{25}}x^{\frac{16}{25}}+x^{\frac{9}{25}}}$$
16
$$\int_0^{\frac{\pi}{2}}\frac{\cos{x}}{2-\cos^2{x}}dx$$
17
$$\int\frac{dx}{(1+x^2)^{\frac{3}{2}}}$$
18
$$\int\frac{dx}{\sqrt{x\sqrt{x}-x^2}}$$
19
$$\int\frac{x-1}{x+x^2\ln{x}}dx$$
20
$$\int\csc{x}\sec{x}dx$$
1
$$\int\frac{x^2}{\sqrt{x^3+2}}dx$$
2
$$\int_1^{\infty}\frac{\ln{x}}{x^2}dx$$
3
$$\int\text{sech}\,(x)dx$$
4
$$\int x^3e^{x^2}dx$$
5
$$\int_0^2\frac{dx}{x\sqrt{x^2-1}}$$
6
$$\int_1^{\infty}\frac{dx}{x(x^2+1)}$$
7
$$\int \cosh^{-1}{(x)}dx$$
8
$$\int_{-\infty}^{\infty}e^{-2x^2-5x-3}dx$$
9
$$\int\sin{\sqrt{x}}dx$$
10
$$\int_0^{\infty}\frac{dx}{\big(x+\frac{1}{x}\big)^2}$$
11
$$\int\frac{(2+x)e^{-x}}{x^3}dx$$
12
$$\int_0^1\frac{dx}{\sqrt{x(1-x)}}$$
13
$$\int_0^{\infty}\frac{\tanh{x}}{e^x}dx$$
14
$$\int_0^{\frac{\pi}{2}}\sqrt{\sin{x}+1}\,dx$$
15
$$\lim_{n\to\infty}I_n\,\text{, where } I_1=\int_0^1\frac{dx}{1+\sqrt{x}}, \,I_2=\int_0^1\frac{dx}{1+\frac{1}{1+\sqrt{x}}}$$
16
$$\int_{-\infty}^{\infty}\frac{\sin^2{\big(x+\frac{\pi}{4}}\big)}{e^{x^2}}dx$$
17
$$\int_{-\infty}^{\infty}3x^2(x^3+1)^2e^{-x^6-2x^3}dx$$
18
$$\int_0^{\frac{\pi}{2}}\frac{dx}{1+\tan^{2017}{x}}$$
19
$$\int e^{2x}\cos{(3x)}dx$$
20
$$\int\cos^{\cos{x}+1}{(x)}\tan{(x)}\big[1+\ln{(\cos{x})}\big]dx$$
1
$$\int\tanh{(x)}dx$$
2
$$\int_{-4}^4|x^3-x|dx$$
3
$$\int_1^e\ln(\sqrt{x})dx$$
4
$$\int\Big(e^{e^x+e^{-x}+x}-e^{e^x+e^{-x}-x}\Big)dx$$
5
$$\int\frac{\ln{(\ln{x})}}{x\ln{x}}dx$$
6
$$\int_0^{\frac{\pi}{3}}\frac{dx}{1+\tan^2{x}}$$
7
$$\int_{-27}^{27}\arcsin{\biggl(\frac{x^{\frac{1}{3}}}{3}\biggl)}dx$$
8
$$\int_{50}^{100}\left\lfloor \log_2{x} \right\rfloor dx$$
9
$$\int(e^x\cos{x}-e^x\sin{x})dx$$
10
$$\int_0^{\infty}x^3e^{-x^2}dx$$
11
$$\int\big[(2e^{x^2}x+1)\cos{x}-(e^x+x)\sin{x}\big]dx$$
12
$$\int(1+x^{\frac{1}{2}}+x^{\frac{1}{3}})(1+x^{-\frac{1}{2}}+x^{-\frac{1}{3}})dx$$
13
$$\int \sin{(\sin{x})\cos{(\sin{x})}}\cos{x}dx$$
14
$$\int\biggl(\frac{\cos{x}+\sin{x}}{x^2}+\frac{\sin{x}-\cos{x}}{x}\biggl)dx$$
15
$$\int x^3\sqrt{x^2+1}\,dx$$
16
$$\int\frac{x}{x^4+x^2+1}dx$$
17
$$\int e^{e^{2016x}+6048x}dx$$
18
$$\int_{\frac{\pi}{3}}^{\frac{\pi}{2}}\frac{1-\cos{x}}{\sin{x}}dx$$
19
$$\int\frac{dx}{1-x+x^2-x^3}$$
20
$$\int_0^{\infty}\frac{dx}{2+\cosh{x}}$$
1
$$\int(\cos^4{x}-\sin^4{x})dx$$
2
$$\int\frac{x}{\sqrt{2+4x}}dx$$
3
$$\int_0^8\frac{\cos{\sqrt{x}}}{\sqrt{x}}dx$$
4
$$\int\sec{(x)}dx$$
5
$$\int_0^{\frac{\pi}{2}}\frac{e^{\sin{x}}}{\tan{x}\csc{x}}dx$$
6
$$\int_1^ex\ln^2{(x)}dx$$
7
$$\int\frac{1}{5+4\sqrt{x}+x}dx$$
8
$$\int(2015)^xdx$$
9
$$\int_0^2\frac{x}{(x-3)(x+5)^2}dx$$
10
$$\int \frac{\ln{(1+\ln{x})}}{x}dx$$
11
$$\int\sqrt{\csc{x}-\sin{x}}\,dx$$
12
$$\int\frac{dx}{\sqrt{x^2+25}}$$
13
$$\int_2^e\frac{\ln^2{x}-1}{x\ln^2{x}}dx$$
14
$$\int e^{3x}\arctan{(e^x)}dx$$
15
$$\int_0^4\frac{|x-1|}{|x-2|+|x-3|}dx$$
16
$$\int_0^{2\pi}\frac{dx}{\sin^4{x}+\cos^4{x}}$$
17
$$\int\frac{1+e^x}{1-e^x}dx$$
18
$$\int\tan^4{(x)}dx$$
19
$$\int\sin{x}\tan^2{(x)}dx$$
20
$$\int\frac{x+1}{x^2+2x+3}dx$$
1
$$\int_1^e\ln{(x^2)}dx$$
2
$$\int_{-9}^9\sin{(\sqrt[3]{x})}dx$$
3
$$\int_0^{\infty}\frac{d}{dx}\big[e^{1+x-x^2}\big]dx$$
4
$$\int_0^2\sqrt{x+\sqrt{x+\sqrt{x+\dots}}}dx$$
5
$$\int \sqrt{x}e^{\sqrt{x}}dx$$
6
$$\int\sin{(2x)}\cos{(3x)}dx$$
7
$$\int_0^{2\pi}|1+2\sin{x}|dx$$
8
$$\int x(1-x)^{2014}dx$$
9
$$\int \text{arcsinh}(x)dx$$
10
$$\int_{-1}^0\frac{x^2}{x-1}dx$$
11
$$\int x\arctan{(x)}dx$$
12
$$\int\frac{dx}{x^2-15x-2014}$$
13
$$\int e^x\big[\ln{(1+x^2)}-2(1+x)\arctan{x}\big]dx$$
14
$$\int \arcsin^2{(x)}dx$$
15
$$\int\frac{\sqrt{x^2-1}}{x}dx$$
16
$$\int x\sec^2{(4x)}dx$$
17
$$\int\frac{2}{6-11x+6x^2-x^3}dx$$
18
$$\int_0^1\frac{1}{\left\lfloor 1-\log_2{(1-x)} \right\rfloor}dx$$
19
$$\int_0^{\frac{1}{\sqrt3}}\sqrt{x+\sqrt{x^2+1}}dx$$
20
$$\int_0^{\frac{5\pi}{2}}\frac{dx}{2+\cos{x}}$$
1
$$\int \big[\ln{(x^2)}-2\ln{(2x)}\big]dx$$
2
$$\int_{-1}^3e^{|x|}dx$$
3
$$\int\frac{\ln{x}\cos{x}-\frac{1}{x}\sin{x}}{\ln^2{x}}dx$$
4
$$\int_1^{11}(x^3-3x^2+3x-1)dx$$
5
$$\int_0^2\sqrt{12-3x^2}dx$$
6
$$\int_0^6\big[x+(x-3)^7+\sin{(x-3)}\big]dx$$
7
$$\int \sin{x}\sqrt{1+\tan^2{x}}\,dx$$
8
$$\int\frac{x^5-x^3+x^2-1}{x^4-x^3+x-1}dx$$
9
$$\int_0^1\ln{x}dx$$
10
$$\int\frac{1}{1-e^{-x}}dx$$
11
$$\int_0^{\pi}\sin^2{x}\cos^2{x}\,dx$$
12
$$\int_0^{441}\frac{\pi\sin{(\pi\sqrt{x})}}{\sqrt{x}}dx$$
13
$$\int\tan^2{x}\,dx$$
14
$$\int_0^{256}(x-\left\lfloor x \right\rfloor)^2dx$$
15
$$\int e^{\sqrt[4]{x}}dx$$
16
$$\int\cos{x\cot{x}}dx$$
17
$$\int(2\ln{x}+\ln^2{x})dx$$
18
$$\int\frac{x^3}{1+x^2}dx$$
19
$$\int\frac{dx}{2-2x+x^2}$$
20
$$\int\sin{x}\ln{(\sin{x})}dx$$
21
$$\int\frac{x}{1-x^4}dx$$
22
$$\int\sqrt{12-3x^2}dx$$
23
$$\int\sec^5{x}\tan^3{x}dx$$
24
$$\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}}\frac{dx}{1-\sin{x}}$$
25
$$\int\frac{dx}{x\sqrt{x^2-2}}$$
1
$$\int\frac{dx}{\sqrt{x}-1}$$
2
$$\int x^{\frac{1}{4}}\ln{(x)}dx$$
3
$$\int\frac{dx}{(1+\sqrt{x})\sqrt{x-x^2}}$$
4
$$\int\frac{dx}{\sqrt{x}(\sqrt[4]{x}+1)^{10}}$$
5
$$\int_0^1\sin{(\arccos{x})}dx$$
6
$$\int\frac{dx}{\sqrt{1-4x-x^2}}$$
7
$$\int_{\frac{1}{4}}^{\frac{1}{2}}\left\lfloor \ln{\left\lfloor \frac{1}{x} \right\rfloor} \right\rfloor dx$$
8
$$\int_0^{\frac{\pi}{8}}\frac{dx}{1+\sin{x}}$$
9
$$\int_1^{2011}\frac{\sqrt{x}}{\sqrt{2012-x}+\sqrt{x}}dx$$
10
$$\int\frac{x-1}{(x+1)\sqrt{x^3+x^2+x}}dx$$
11
$$\int_{-1}^0\frac{x^4+4x^3+6x^2+4x+1}{x^3-3x^2+3x-1}dx$$
12
$$\int\biggl(\cos{x}\ln{x}+\frac{\sin{x}}{x}\biggl)dx$$
13
$$\int\frac{dx}{x^3-x}$$
14
$$\int_0^{\frac{1}{2}}\frac{x\arcsin{x}}{\sqrt{1-x^2}}dx$$
15
$$\int_0^1x(1-x)^{99}dx$$
16
$$\int_0^{\frac{\pi}{2}}\frac{\sin{4x}}{\sin{x}}dx$$
17
$$\int\frac{x^{-\frac{1}{2}}}{1+x^{\frac{1}{3}}}dx$$
18
$$\int\frac{dx}{\sqrt{2x^2-1}}$$
19
$$\int\frac{dx}{\sqrt{e^x-1}}$$
20
$$\int\frac{x}{x^4+4}dx$$
21
$$\int\frac{2dx}{(\cos{x}-\sin{x})^2}$$
22
$$\int\frac{x\cosh{x}}{\sinh{x^2}}dx$$
23
$$\int_0^2x^5\sqrt{1+x^3}dx$$
24
$$\int_0^1\frac{x^7-1}{\ln{x}}dx$$
25
$$\int\sqrt{\csc{x}-\sin{x}}\,dx$$
1
$$\int\frac{x^6-1}{x^4+x^3-x-1}dx$$
2
$$\int (2\ln{x}+\ln^2{x})dx$$
3
$$\int 2\frac{x}{\sqrt{1-x^4}}dx$$
4
$$\int\frac{x^2+1}{x+1}dx$$
5
$$\int\frac{\sin^3{x}+\sin^2{x}-2\sin{x}-2}{\sin^2{x}+2\sin{x}+1}dx$$
6
$$\int \sinh{(x^{-2})}dx$$
7
$$\int\sec^4{(x)}\tan^2{(x)}dx$$
8
$$\int\sqrt{\csc{x}-\sin{x}}\,dx$$
9
$$\int\cos^6{x}dx$$
10
$$\int\frac{dx}{1+2x^2+x^4}$$
11
$$\int\cos{(\ln{x})}dx$$
12
$$\int\frac{1}{\cos{x}}dx$$
13
$$\int\frac{dx}{9\cos^2{x}+4\sin^2{x}}$$
14
$$\int\frac{dx}{x^2(x^4+1)^{\frac{3}{4}}}$$
15
$$\int_0^{\pi}\cos{(x)}\cos{(3x)}\cos{(5x)}dx$$
16
$$\int\Big[\frac{1}{\ln{x}}+\ln{(\ln{x})}\Big]dx$$
17
$$\int\frac{dx}{2+e^x}$$
18
$$\int\sqrt{\frac{x}{1-x^3}}dx$$
19
$$\int\frac{4x}{1-x^4}dx$$
20
$$\int x^x(1+\ln{x})dx$$
21
$$\int_0^6\sqrt{6x-x^2}\,dx$$
22
$$\int\sin{(101x)}\sin^{99}{x}dx$$
23
$$\int xe^{e^{x^2}+x^2}dx$$
24
$$\int_0^1\frac{x^3-3x^2+3x-1}{x^4+4x^3+6x^2+4x+1}dx$$
25
$$\int\sqrt{\frac{1-x}{1+x}}dx$$
1
$$\int_0^{\frac{\pi}{2}}\sin{(x)}\sin{(2x)}\sin{(3x)}dx$$
2
$$\int_0^{\frac{\pi}{2}}\sin^3{(2x)}\cos{(x)}dx$$
3
$$\int(x+1)^2(x-1)^{\frac{1}{3}}dx$$
4
$$\int x\ln{\Big(1+\frac{1}{x}\Big)}dx$$
5
$$\int_0^1\sin^2{(\ln{x})}dx$$
6
$$\int\frac{dx}{1+3e^x}$$
7
$$\int_{\frac{\pi}{4}}^{\frac{\pi}{3}}\frac{dx}{\sin^3{x}\cos^5{x}}$$
8
$$\int_1^{\infty}\frac{dx}{x\sqrt{x^4-1}}$$
9
$$\int\frac{dx}{x(x^5+1)}$$
10
$$\int_0^{\frac{\pi}{4}}\sqrt{\tan{x}}\,dx$$
11
$$\int_0^1\frac{\ln{(1+x)}}{1+x^2}dx$$
12
$$\int_{64}^{729}\frac{x^{\frac{1}{2}}}{x^{\frac{1}{2}}-x^{\frac{1}{3}}}dx$$
13
$$\int x^x(1+\ln{x})dx$$
14
$$\int_0^1x^{\frac{13}{2}}\sqrt{1+x^{\frac{5}{2}}}\,dx$$
15
$$\int_1^{\infty}\frac{dx}{(x^2+1)^2}$$
16
$$\int_0^1\frac{dx}{x^4-13x^2+36}$$
17
$$\int\frac{\ln{(\ln{x})}}{x}dx$$
18
$$\int\frac{1+\cot{x}}{1-\cot{x}}dx$$
19
$$\int\frac{\cos{x}+x\sin{x}}{x(x+\cos{x})}dx$$
20
$$\int_0^{\frac{\pi}{2}}\frac{dx}{\sin{x}+\sec{x}}$$
21
$$\int_0^{\infty}\frac{dx}{\sqrt{1+e^x+e^{2x}}}$$
22
$$\int_0^1x^3e^{x^2}dx$$
23
$$\int_0^1\sqrt{1+x\sqrt{1+x\sqrt{1+x\sqrt{\dots}}}}dx$$
24
$$\int\biggl(\frac{1}{\ln{x}}-\frac{1}{\ln^2{x}}\biggl)dx$$
25
$$\int_1^2(x-1)^{\frac{1}{2}}(2-x)^{\frac{1}{2}}dx$$