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Prove $\int_0^1 \frac{dx}{(x-2) \sqrt[5]{x^2{(1-x)}^3}} = -\frac{2^{\frac{11}{10}} \pi}{\sqrt{5+\sqrt{5}}}$

How to evaluate $I=\int_0^\pi\frac{\cos(\theta+\alpha)\sin(\theta)d\theta}{\sqrt{r^2+a^2-2ra\cos(\theta)}}$

Solve $\int_{0}^{\pi/2} \arccos\left( \frac{\cos(x)}{1+2\cos(x)} \right) \mathrm dx$ [closed]

How to evalute $\int_{0}^{1}\frac{x\log x}{\log(1-x)}dx$

Integral: $\int_0^{\infty} \cos\left(\frac{a^2}{x^2}-b^2x^2\right)\,dx$ for $a,b>0$

Is the integral always the area under the curve?

How evaluate the following hard integrals?

How to Integrate this function $\int(1-x^2)^ndx$

Evaluate $\int_{0}^{1/2}\frac{e^x(2-x^2)}{(1-x)^{3/2}(1+x)^{1/2}}\,dx$

More general Frullani's [closed]

Conjectured closed form for $\int_0^1\frac{\operatorname{li}^4(x)}{x^4}\,dx$

Integral $\int_0^1(x(1-x))^n\frac{d^n}{d^n x}(\log x \cdot\log (1-x))dx$

Get a good approximation of $\int_0^1 \left(H_x\right)^2 dx$, where $H_x$ is the generalized harmonic number

Can the infinite sum $\sum_{n=0}^\infty {2^n \sum_{k=0}^n (-1)^k \frac{ {{n}\choose{k}}}{ (n+k)! }}$ be simplified?

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Evaluate $\int_0^1 x^{a-1}(1-x)^{b-1}\operatorname{Li}_3(x) \, dx$

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A solution for $\int^{2\pi}_0e^{\cos \theta}\cos(a\theta -\sin \theta)\,d \theta $

Integral of $1 / \sqrt x$ using Limits

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Evaluate $\sum _{n=1}^{\infty } \frac{1}{n^5 2^n \binom{3 n}{n}}$ in terms of elementary constants

Prove $\int_0^1 \frac{dx}{(x-2) \sqrt[5]{x^2{(1-x)}^3}} = -\frac{2^{\frac{11}{10}} \pi}{\sqrt{5+\sqrt{5}}}$

How to evaluate $I=\int_0^\pi\frac{\cos(\theta+\alpha)\sin(\theta)d\theta}{\sqrt{r^2+a^2-2ra\cos(\theta)}}$

Solve $\int_{0}^{\pi/2} \arccos\left( \frac{\cos(x)}{1+2\cos(x)} \right) \mathrm dx$ [closed]

How to evalute $\int_{0}^{1}\frac{x\log x}{\log(1-x)}dx$

Integral: $\int_0^{\infty} \cos\left(\frac{a^2}{x^2}-b^2x^2\right)\,dx$ for $a,b>0$

Is the integral always the area under the curve?

How evaluate the following hard integrals?

How to Integrate this function $\int(1-x^2)^ndx$

Evaluate $\int_{0}^{1/2}\frac{e^x(2-x^2)}{(1-x)^{3/2}(1+x)^{1/2}}\,dx$

More general Frullani's [closed]

Conjectured closed form for $\int_0^1\frac{\operatorname{li}^4(x)}{x^4}\,dx$

Integral $\int_0^1(x(1-x))^n\frac{d^n}{d^n x}(\log x \cdot\log (1-x))dx$

Get a good approximation of $\int_0^1 \left(H_x\right)^2 dx$, where $H_x$ is the generalized harmonic number

Can the infinite sum $\sum_{n=0}^\infty {2^n \sum_{k=0}^n (-1)^k \frac{ {{n}\choose{k}}}{ (n+k)! }}$ be simplified?