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 22 How to evaluate $\int\frac{1+x^4}{(1-x^4)^{3/2}}dx$? 18 A difficult double integral $\int_{0}^{1}\int_{0}^{1}\frac{x\ln x \ln y }{1-xy}\frac{dxdy}{\ln(xy)}$ 16 Integral $\int_0^{2π} e^{e^{ix}} dx$ 15 Integral $\int_0^\infty \frac{\ln x}{(x+c)(x-1)} dx$ 15 Integral $\int_{0}^{\frac{\pi}4} \ln(\sin{x}+\cos{x}+\sqrt{\sin{2x}})dx$

### Reputation (18,126)

 +10 An AMM-like integral $\int_0^1\frac{\arctan x}x\ln\frac{(1+x^2)^3}{(1+x)^2}dx$ +10 Integrate $\int_{0}^\infty \frac{\tanh(x)}{x^3}-\frac{\operatorname{sech}(x)}{x^2}dx$ +10 Solving the integral $\int \ln\left ( \frac{1+\sqrt{1-x^2}}{1-\sqrt{1-x^2}} \right ) \frac{dx}{1-x^2}$ +10 Integral $\int_{-\infty}^{\infty} \arctan(e^x) \arctan(e^{-x})dx=\frac{7}{4}\zeta(3)$

### Questions (79)

 35 Relation between the roots of a function 34 Integral for the New Year $2019$! 33 Proving that $\int_0^1 \frac{\arctan x}{x}\ln\left(\frac{1+x^2}{(1-x)^2}\right)dx=\frac{\pi^3}{16}$ 24 Integral $\int_0^\infty \frac{\ln x}{(\pi^2+\ln^2 x)(1+x)^2} \frac{dx}{\sqrt x}$ 24 Integral $\int_0^1 \frac{dx}{\prod_{n=1}^\infty (1+x^n)}$

### Tags (97)

 999 integration × 228 93 sequences-and-series × 27 720 definite-integrals × 146 70 indefinite-integrals × 15 424 calculus × 71 60 logarithms × 13 199 closed-form × 61 55 real-analysis × 11 193 improper-integrals × 35 42 riemann-zeta × 9