MIT Integration Bee 2017 problem:$\int_0^{\pi/2}\frac 1 {1+\tan^{2017} x} \, dx$ : Need hints
9653
Evaluate the integral $\int^{\frac{\pi}{2}}_0 \frac{\sin^3x}{\sin^3x+\cos^3x}\,\mathrm dx$.
47206
$-1 = 0$ by integration by parts of $\tan(x)$
20016
How to integrate $\int_0^{\pi/2}\frac{\sin^nx}{\sin^nx+\cos^nx}dx$?
31063
Evaluating $\int_0^2(\tan^{-1}(\pi x)-\tan^{-1} x)\,\mathrm{d}x$
62450
Computing $ \int_0^{2\pi} \frac{1}{a^2\cos^2 t+b^2 \sin^2 t} dt \;; a,b>0$.
16800
Integrating $\int_0^{2\pi} \frac1{a\cos(t)+b\sin(t)+c}dt$ with $\sqrt{a^2+b^2}=1<c$
106544
Solve $ \frac{2}{\pi}\int_{-\pi}^\pi\frac{\sin\frac{9x}{2}}{\sin\frac{x}{2}}dx $
151063
Calculate $\int_{0}^{\frac{\pi}{2}}\frac{\sin^{3}(t)}{\sin^{3}(t)+\cos^{3}(t)}dt$ by hands
130670
Solving Integrals
49489
Compute $\lim_{n\to\infty} \int_{0}^{\pi/4}\tan^n x \ dx$
105496
Need help solving - $ \int (\sin 101x) \cdot\sin^{99}x\,dx $
147113
How to solve $2 \tan x / (1 - (\tan x)^2) = (\sin 2x)^2$?
119815
Why is $\tan((1/2)\pi)$ undefined?
44398
How to compute $\int_0^{\pi/2}\frac{\sin^3 t}{\sin^3 t+\cos^3 t}dt$?
122843
Finding $\int_0^\infty \frac{\cos(ax)-\cos(bx)}{x}dx$
6717
Evaluation of $\int_{\frac{1}{2014}}^{2014} \frac{\tan^{-1}x}{x} dx$
124401
How to evaluate $\int_0^{2\pi}\frac{1}{(1+a\cos {\theta})^2}\,d\theta$ without contour integration?