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Let $A=\pi^2\int_{0}^{1}\frac{\sin(\pi x)}{1 + \sin(\pi x)}dx$ and $B=\int_{0}^{\pi}\frac{x\sin( x)}{1 + \sin( x)}dx$. Find $\frac{A}{B}$.

Show that $\int_{0}^{1} \frac{\ln|x+1|}{x^2+1}dx= \frac\pi8 \ln2$ using a suitable substitution

How to evaluate the following interesting integral?

Finding the closed form of $\int_0^1 \frac{(1-x+x\log x)\operatorname{Li}_3(x)}{x(x-1) \log x} \ dx$

Compute $\int_0^1 \frac{\mathrm{d}x}{\sqrt{1-x^4}} \cdot \int_0^1 \frac{x^2\mathrm{d}x}{\sqrt{1-x^4}}$

Formulae for Catalan's constant.

Show $\int_0^\infty f\left(x+\frac{1}{x}\right)\,\frac{\ln x}{x}\,dx=0$ if $f(x)$ is a bounded non-negative function

Evaluate $\int_0^1\frac{\ln(1-x)\ln(1+x)}{1+x^2}dx$

Conjectured value of a difficult integral with Dedekind eta functions

Arctangent integral that I'm having difficulty on

Show that $\int_0^1 \prod_{n\geq 1} (1-x^n) \, dx = \frac{4\pi\sqrt{3}\sinh(\frac{\pi}{3}\sqrt{23})}{\sqrt{23}\cosh(\frac{\pi}{2}\sqrt{23})}$ [duplicate]

Why is this integral diverging? $\int\limits^{\infty}_{-\infty} \,\frac{x}{x^2+1} dx$

Value of this definite integral $\int_{0}^{\infty} \frac{ \ln(x)}{x^2+2x+4} dx $

Understanding Limits of Integration in Integration-by-Parts

Why am I getting 2 different answers for Integral exp(ix) from 0 to Infinity

New posts in definite-integrals

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$ \int_0^\frac{\pi}{2}\ln^n\left(\tan(x)\right)\:dx$

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How to compute $\int_0^{+\infty} \frac{dt}{1+t^4} = \frac{\pi}{2\sqrt 2}.$

Evaluating $\frac{1}{\pi} \int_{0}^{\pi} e^{2\cos{\theta}} d\theta$

Let $A=\pi^2\int_{0}^{1}\frac{\sin(\pi x)}{1 + \sin(\pi x)}dx$ and $B=\int_{0}^{\pi}\frac{x\sin( x)}{1 + \sin( x)}dx$. Find $\frac{A}{B}$.

Show that $\int_{0}^{1} \frac{\ln|x+1|}{x^2+1}dx= \frac\pi8 \ln2$ using a suitable substitution

How to evaluate the following interesting integral?

Finding the closed form of $\int_0^1 \frac{(1-x+x\log x)\operatorname{Li}_3(x)}{x(x-1) \log x} \ dx$

Compute $\int_0^1 \frac{\mathrm{d}x}{\sqrt{1-x^4}} \cdot \int_0^1 \frac{x^2\mathrm{d}x}{\sqrt{1-x^4}}$

Formulae for Catalan's constant.

Show $\int_0^\infty f\left(x+\frac{1}{x}\right)\,\frac{\ln x}{x}\,dx=0$ if $f(x)$ is a bounded non-negative function

Evaluate $\int_0^1\frac{\ln(1-x)\ln(1+x)}{1+x^2}dx$

Conjectured value of a difficult integral with Dedekind eta functions

Arctangent integral that I'm having difficulty on

Show that $\int_0^1 \prod_{n\geq 1} (1-x^n) \, dx = \frac{4\pi\sqrt{3}\sinh(\frac{\pi}{3}\sqrt{23})}{\sqrt{23}\cosh(\frac{\pi}{2}\sqrt{23})}$ [duplicate]

Why is this integral diverging? $\int\limits^{\infty}_{-\infty} \,\frac{x}{x^2+1} dx$

Value of this definite integral $\int_{0}^{\infty} \frac{ \ln(x)}{x^2+2x+4} dx $

Understanding Limits of Integration in Integration-by-Parts

Why am I getting 2 different answers for Integral exp(ix) from 0 to Infinity