Finding $\min \frac{\left[\int_{0}^{1}f(x)\mathrm dx\right]^2}{\int_{0}^{1}(f(x))^3\mathrm dx}$ given that $f(0)=0$ and $0\lt f'(x)\le 1$
133851
How to arrive at $\int_{0}^{1} f^3(x) \, dx < (\int_{0}^{1} f(x) \, dx)^2$?
112621
Finding $\int_{0}^{\infty} \frac{e^{3x}-e^x}{x(e^{3x}+1)(e^x+1)} dx$
22294
Maximum and minimum value of $\int_0^1 f(x)dx $ given $|f'(x)|<2$
27347
Verify that $\left|\int_{\gamma} \exp(iz^2)dz\right| \leq \frac{\pi\big(1-\exp(-r^2)\big)}{4r}$ where $\gamma(t)=re^{it}$, for $0\leq t \leq \pi/4$.
59352
Computing: $\int_0^1 \sqrt[3]{x\log{\frac{1}x}} \, \mathrm dx$
19716
What is $\int_0^1\frac{x^7-1}{\log(x)}\mathrm dx$?
79466
Evaluating $\int_0^1 \log \log \left(\frac{1}{x}\right) \frac{dx}{1+x^2}$
138174
Integral $\int_0^1 \frac{x\ln\left(\frac{1+x}{1-x}\right)}{\left(\pi^2+\ln^2\left(\frac{1+x}{1-x}\right)\right)^2}dx$
142682
Find $f(x)$ where $ f(x)+f\left(\frac{1-x}x\right)=x$
87395
Evaluating $\int_{I^n} \left( \min_{1\le i \le n}x_i \right)^{\alpha}\,\, dx$
93806
$\|f\|_{L^{p}}=\sup\left\{\int_{{\bf R}^{n}}|f(x)g(x)|~dx:\|g\|_{L^{q}}\le1\right\}$
144146
find a $\int_{x}^{g(x)} f(t)\,dt = 1$
91333
How to find $\int_{0}^{1}\dfrac{\ln^2{x}\ln^2{(1-x)}}{2-x}dx$
52982
Efficient/faster methods to find the general closed form of $\int _0^1\frac{\ln \left(ax^2+b\right)}{x+1}\:dx$
77983
Shortest method for $\int_{0}^{1}\frac{x^{4}\left(1-x\right)^{4}}{1+x^{2}}$
155415
Minimax problem for optimization $\inf \sup \frac{x f(x)}{\int_0^1 f(t) dt}$
122361
Evaluate $\int_0^1\left(\frac{1}{\ln x} + \frac{1}{1-x}\right)^2 \mathrm dx$