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A reason for $ 64\int_0^1 \left(\frac \pi 4+\arctan t\right)^2\cdot \log t\cdot\frac 1{1-t^2}\; dt =-\pi^4$ ...

How to find the closed form of the integral$\int_{0}^{\infty}f(x)\frac{\sin^nx}{x^m}dx$

Closed form for integral of inverse hyperbolic function in terms of ${_4F_3}$

How to evaluate integral $\int_{0}^{\infty} \left(\frac{1-e^{-x}}{x}\right)^n dx$.

Prove that $\lim_{n\to\infty}n^2\int_0^{\frac{1}{n}}x^{x+1}dx=\frac{1}{2}.$

Continued fraction for some integrals by Ramanujan

How to evaluate the integral $\int_0^{2\pi} \theta\exp(x\cos(\theta) + y\sin(\theta))) d\theta$

Feynman Parameters

Evaluating $\int_0^\infty\frac{\ln(1+x^2)}{e^{\pi x}-1}dx$

Evaluating $\int_{0}^{1} x^m \ln^\alpha(x) dx$

Computing $\sum_{n=1}^{\infty} \frac{\psi\left(\frac{n+1}{2}\right)}{ \binom{2n}{n}}$

Evaluate $ \int_{0}^{1}{\frac{\ln{x}}{x^2-x-1}dx}$

How to find $\int_{0}^{\pi/2} \log ({1+\cos x}) dx$ using real-variable methods?

Integral $I=\int_0^\infty \frac{\ln(1+x) \operatorname{Li}_2 (-x)}{x^{3/2}} dx$

Evaluating $\int_{-\infty}^\infty \frac{\sin x}{x-i} dx$

How to Integrate $ \int^{\pi/2}_{0} x \ln(\cos x) \sqrt{\tan x}\,dx$

Logarithmic Integral II

New posts in definite-integrals

Integral with messy integrand

Mean Value Theorem Integrals

Compute the value of the integral $\int_1^{\infty} \lfloor x^2 \rfloor e^{-x} \ \mathrm d x $

A reason for $ 64\int_0^1 \left(\frac \pi 4+\arctan t\right)^2\cdot \log t\cdot\frac 1{1-t^2}\; dt =-\pi^4$ ...

How to find the closed form of the integral$\int_{0}^{\infty}f(x)\frac{\sin^nx}{x^m}dx$

Closed form for integral of inverse hyperbolic function in terms of ${_4F_3}$

How to evaluate integral $\int_{0}^{\infty} \left(\frac{1-e^{-x}}{x}\right)^n dx$.

Prove that $\lim_{n\to\infty}n^2\int_0^{\frac{1}{n}}x^{x+1}dx=\frac{1}{2}.$

Continued fraction for some integrals by Ramanujan

How to evaluate the integral $\int_0^{2\pi} \theta\exp(x\cos(\theta) + y\sin(\theta))) d\theta$

Feynman Parameters

Evaluating $\int_0^\infty\frac{\ln(1+x^2)}{e^{\pi x}-1}dx$

Evaluating $\int_{0}^{1} x^m \ln^\alpha(x) dx$

Computing $\sum_{n=1}^{\infty} \frac{\psi\left(\frac{n+1}{2}\right)}{ \binom{2n}{n}}$

Evaluate $ \int_{0}^{1}{\frac{\ln{x}}{x^2-x-1}dx}$

How to find $\int_{0}^{\pi/2} \log ({1+\cos x}) dx$ using real-variable methods?

Integral $I=\int_0^\infty \frac{\ln(1+x) \operatorname{Li}_2 (-x)}{x^{3/2}} dx$

Evaluating $\int_{-\infty}^\infty \frac{\sin x}{x-i} dx$

How to Integrate $ \int^{\pi/2}_{0} x \ln(\cos x) \sqrt{\tan x}\,dx$

Logarithmic Integral II