UNSW MathSoc Bee Qualification
1
$$\int\frac{dx}{1-e^{-2022x}}$$
2
$$\int\frac{\tan^3{(1+\ln{x})}}{x}dx$$
3
$$\int\frac{dx}{2-2x+x^2}$$
4
$$\int_{-1}^0\frac{15165}{2}x\sqrt{1+x}\,dx$$
5
$$\int_0^1(x-3^x)^2dx$$
6
$$\int\frac{x^{12}}{x^2+1}dx$$
7
$$\int\frac{x^2}{(x-1)(x^2+x+1)}dx$$
8
$$\int\frac{\sin{2x}}{1+2\sin^2{x}}dx$$
9
$$\int_0^1(2x-1)\frac{\sqrt{x}+\sqrt{1-x}}{\sqrt{x}-\sqrt{1-x}}dx$$
10
$$\int\frac{2\cos{x}-2\sin{x}}{2+\sin{2x}}dx$$
11
$$\int_0^ex^{\frac{1}{\ln{x}}}dx$$
12
$$\int\sqrt{x\sqrt{x\sqrt{x\dots}}}dx$$
13
$$\int_1^2x^{x^2+1}(2\ln{x}+1)dx$$
14
$$\int_0^{2022\pi}\sin{(\sin{x}-x)}dx$$
15
$$\int_0^1x\tan^{-1}{(x^2-1)}dx$$
16
$$\int\frac{dx}{\sqrt{x\sqrt{x}-x^2}}$$
17
$$\int_1^{e^2}(\ln{(x^{\ln{x}-6})}+5)x^3dx$$
18
$$\int_0^{\pi/2}\frac{dx}{\tan^{\sqrt{2022}}{(x)}+1}$$
19
$$\int_0^1\sqrt{x+\sqrt{x+\sqrt{x+\dots}}}dx$$
20
$$\int_0^{\frac{\pi}{2}}\prod_{k=1}^7\cos{kx}\,dx$$
1
$$\int\frac{dx}{x\log_{10}{x}}$$
2
$$\int_0^{2\pi}(x-\pi)^3\cos{x}\,dx$$
3
$$\int_{-2}^4e^{|x|}dx$$
4
$$\int\Big(\arctan{x}+\frac{x}{1+x^2}\Big)dx$$
5
$$\int \sec^3{(\sqrt{x})}dx$$
6
$$\int_0^{\frac{\pi}{2}}\big[\ln{(\sec{x}-1)}+\ln{(\sec{x}+1)}\big]dx$$
7
$$\int\frac{\sin{x}-x}{1-\cos{x}}dx$$
8
$$\int\frac{dx}{1+\cos^2{x}}$$
9
$$\int_0^{\pi}\frac{x\sin{x}}{1+\cos^2{x}}dx$$
10
$$\int_{\sqrt[3]{2}}^{\sqrt[3]{3}}(3x^{14}-12x^{11}+18x^8-12x^5+3x^2)dx$$
11
$$\int\frac{dx}{\sqrt{1+e^x}}$$
12
$$\int e^{\sin{x}}(\cos^2{x}-\sin{x})dx$$
13
$$\int_{-\pi}^{\pi}\left\lfloor \sin{(\sin{2x})} \right\rfloor dx$$
14
$$\int\frac{dx}{x^{101}+x}$$
15
$$\int_0^{\frac{\pi}{4}}\frac{\sec{x}}{\sqrt{1+\sin{2x}}}dx$$
1
$$\int_{503}^{507}xdx$$
2
$$\int 3^{\ln{x}}dx$$
3
$$\int {\sqrt{e^x}}dx$$
4
$$\int\sqrt{e^x-1}\,dx$$
5
$$\int\cos{(\ln{x})}dx$$
6
$$\int\frac{e^{2x}}{\sqrt{1-e^{4x}}}dx$$
7
$$\int_{-\frac{7\pi}{4}}^{\frac{7\pi}{4}}\frac{4x\cos{x}}{-\sin{|x|}+\cos{|x|}}dx$$
8
$$\int_0^{\frac{\pi}{2}}\frac{\sin^k{x}}{\sin^k{x}+\cos^k{x}}dx$$
9
$$\int\frac{e^x}{1+e^{2x}}dx$$
10
$$\int \sec^2{(x)}\sec^2{(\tan{x})}\sec^2{(\tan{(\tan{x})})}dx$$
11
$$\int_0^2\Big(\left\lfloor x \right\rfloor-2\left\lfloor \frac{x}{2} \right\rfloor\Big)dx$$
12
$$\int_0^{\frac{\sqrt3}{4}}\frac{2x\arcsin{(2x)}}{\sqrt{1-4x^2}}dx$$
13
$$\int_0^1\arcsin{\sqrt{x}}\,dx$$
14
$$\int_0^{\frac{\pi}{2}}\frac{1}{1+\tan^4{x}}dx$$
15
$$\int_0^{\frac{3\pi}{2}}\arcsin{(\sin{x})dx}$$
16
$$\int_1^{\infty}\frac{dx}{x(x^2+1)}$$
17
$$\int_0^{\frac{\pi}{2}}\frac{dx}{1+\sin{x}}$$
18
$$\int e^{\cos^{-1}{x}}dx$$
19
$$\int_0^{\frac{\pi}{2}}\frac{25}{(3\cos{x}+4\sin{x})^2}dx$$
20
$$\int\frac{dx}{x^7+x}$$
1
$$\int \Big(e^x\ln{x}+\frac{e^x}{x}\Big)dx$$
2
$$\int_{-1}^{1}(\text{arccos}\,x+\arcsin{x})dx$$
3
$$\int_{1160}^{1163}2x\,dx$$
4
$$\int_0^{\infty}x^ne^{-x}dx\,\,,\,\small{n\in\mathbb{Z_+}}$$
5
$$\int_0^{\infty}\frac{e^{2x}}{1+e^{4x}}dx$$
6
$$\int e^{2019x}\cos{(2019x)}dx$$
7
$$\int_{-2019}^0\sqrt{4076361-x^2}\,dx$$
8
$$\int 2019^{2019x}dx$$
9
$$\int\frac{\sin{4x}}{\sin{x}}dx$$
10
$$\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\frac{2x\sin{|x|}}{5+\cos{4x}}dx$$
11
$$\int_0^{\frac{\pi}{2}}\frac{5\cos{x}}{3\sin{x}+4}dx$$
12
$$\int \cos{x}\cos{(\sin{x})}\cos{(\sin{(\sin{x})})}dx$$
13
$$\int_{-9\pi}^{2019\pi}\arcsin{(\sin{x})}dx$$
14
$$\int_0^1x^3(1-x)^7dx$$
15
$$\int_0^{\frac{\pi}{2}}\sin{x}\sin{2x}\sin{3x}dx$$
16
$$\int_0^{\frac{\pi}{2}}\ln{(\tan{x})}dx$$
17
$$\int_{-\frac{\pi}{4}}^{\frac{\pi}{24}}(8\text{cot}\,8x+4\tan{4x}+2\tan{2x}+\tan{x}-\text{cot}\,x)dx$$
18
$$\int\frac{dx}{(x^2-2x)(x^2-2x+1)(x^2-2x+2)}$$
19
$$\int_{-3}^{3}\frac{x^4}{e^x+1}dx$$
20
$$\int_{-2}^2\frac{|x-2|+|x|+|x+2|}{|x-1|+|x+1|}dx$$
21
$$\int_{-1}^{1}\frac{e^{2x}+1-(x+1)(e^x+e^{-x})}{x(e^x-1)}dx$$
22
$$\int\sqrt{1+\frac{1}{x}}\,dx\,\,,\,\small{x>0}$$
23
$$\int_0^{\frac{\pi}{4}}\sec^5{x}dx$$
24
$$\int_{-4}^0\frac{\sqrt{\ln{(5-2x)}}}{\sqrt{\ln{(5-2x)}}+\sqrt{\ln{(2x+13)}}}dx$$
25
$$\int\frac{x\cos{x}+1}{\sqrt{2x^3e^{\sin{x}}+x^2}}dx$$
26
$$\int_0^{\frac{\pi}{2}}\sqrt{\tan{x}}\,dx$$
27
$$\int_0^{\pi}\frac{\sin{\frac{2019x}{2}}}{\sin{\frac{x}{2}}}dx$$
28
$$\int_0^1\ln{x}\arcsin{x}\,dx$$
29
$$\int_0^{\infty}\frac{x-1}{\sqrt{2^x-1}\ln{(2^x-1)}}dx$$