# Tagged Questions

2answers
93 views

### Integral $\int_0^{\Large\frac{\pi}{4}}\left(\frac{1}{\log(\tan(x))}+\frac{1}{1-\tan(x)}\right)dx$

I am wondering if anyone would know how to evaluate this integral: $$\int_{0}^{\Large\frac{\pi}{4}}\left(\frac{1}{\log(\tan(x))}+\frac{1}{1-\tan(x)}\right)dx.$$ I've tried, unsuccessfully, the change ...
2answers
74 views

### Integrals of integer powers of dilogarithm function

I'm interested in evaluating integrals of positive integer powers of the dilogarithm function. I'd like to see the general case tackled if possible, or barring that then as many particular cases as ...
2answers
86 views

### Integral $\int_{0}^1 \sqrt{\frac{\ln{x}}{x^2-1}} dx$

Please help evaluating this integral $$\large\int_{0}^1 \sqrt{\frac{\ln{x}}{x^2-1}} dx$$ Mathematica could not evaluate it in a closed form. Numerically it is about ...
0answers
63 views

### Contour Integral $\int_{0}^1 \frac{\ln{x}}{\sqrt{1-x^2}} \mathrm dx$

I need help evaluating this with contour integration$$\int_{0}^1 \frac{\ln{x}}{\sqrt{1-x^2}} \mathrm dx$$ I am not sure as to how to work with the branch cuts of both $\ln{x}$ and $\sqrt{1-x^2}$ ...
2answers
57 views

### A identity relating a infinite series and a definite integral [duplicate]

Prove that, $$\sum_{n=1}^{\infty} \frac{1}{n^n} = \int_{0}^{1} x^{-x}dx$$ I made no significant progress, I'm looking for hint/ideas to approach this problem. Thanks!
3answers
103 views

### Integral of $\ln(x)\operatorname{sech}(x)$

How can I prove that: ...
3answers
146 views