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Showing that $\displaystyle\int_{-a}^{a} \frac{\sqrt{a^2-x^2}}{1+x^2}dx = \pi\left (\sqrt{a^2+1}-1\right)$.

Derivative of definite integral

Integrating $\int_0^1\frac{x\ln (1+x)}{1+x^2}dx$ with restricted techniques

How can I prove $\int_{0}^{1} \frac {x-1}{\log(x) (1+x^3)}dx=\frac {\log3}{2}$

A sine inverse integral

Finding $\int_{-2}^8xf(x)dx$ given $\int_{-2}^8f(x)dx$

Convergence of the sequence $a_n=\int_0^1{nx^{n-1}\over 1+x}dx$ [duplicate]

Prove $\int_{\frac{\pi}{20}}^{\frac{3\pi}{20}} \ln \tan x\,\,dx= - \frac{2G}{5}$

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

What is the value of the integral$\int_{0}^{+\infty} \frac{1-\cos t}{t} \, e^{-t} \, \mathrm{d}t$?

Prove that $f(1)-f(1/e)\le \int_0^1 \sqrt{x} f'(x) dx$

Closed form of $\int_0^1 \tan(\gamma\sqrt{1-x^2}) dx$

Prove $\int_0^\infty\Big|\Gamma\Big(\frac13+\frac{i\alpha}{\pi}\Big)\Big|^6\alpha \sinh\alpha~d\alpha=\frac{\pi\sqrt{27}}{4}\Gamma^9\Big(\frac23\Big)$

Generalized sine integral $ \int_0^\infty \sin^m(x^n)/x^p\,\mathrm dx$

Why is $\int_{-\infty}^\infty \frac{1}{\sinh^2(t-i)} dt = -2$?

Formula for a sequence defined on $K_1(x,y) := y+0$ if $x \geq y$ and $y-1$ otherwise

New posts in definite-integrals

Evaluate $\int_0^1(x\ln(x))^{50}dx$

If $\int_1^ \infty \frac {x^3+3}{x^6(x^2+1)} \, \mathrm d x=\frac{a+b\pi}{c}$, then find $a,b,c$.

compute: $\int_{0}^{1}e^x(1-x)^{100}dx$

Solving $\int e^{kx}(f(x)+f'(x))\, dx.$

Showing that $\displaystyle\int_{-a}^{a} \frac{\sqrt{a^2-x^2}}{1+x^2}dx = \pi\left (\sqrt{a^2+1}-1\right)$.

Derivative of definite integral

Integrating $\int_0^1\frac{x\ln (1+x)}{1+x^2}dx$ with restricted techniques

How can I prove $\int_{0}^{1} \frac {x-1}{\log(x) (1+x^3)}dx=\frac {\log3}{2}$

A sine inverse integral

Finding $\int_{-2}^8xf(x)dx$ given $\int_{-2}^8f(x)dx$

Convergence of the sequence $a_n=\int_0^1{nx^{n-1}\over 1+x}dx$ [duplicate]

Prove $\int_{\frac{\pi}{20}}^{\frac{3\pi}{20}} \ln \tan x\,\,dx= - \frac{2G}{5}$

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

What is the value of the integral$\int_{0}^{+\infty} \frac{1-\cos t}{t} \, e^{-t} \, \mathrm{d}t$?

Prove that $f(1)-f(1/e)\le \int_0^1 \sqrt{x} f'(x) dx$

Closed form of $\int_0^1 \tan(\gamma\sqrt{1-x^2}) dx$

Prove $\int_0^\infty\Big|\Gamma\Big(\frac13+\frac{i\alpha}{\pi}\Big)\Big|^6\alpha \sinh\alpha~d\alpha=\frac{\pi\sqrt{27}}{4}\Gamma^9\Big(\frac23\Big)$

Generalized sine integral $ \int_0^\infty \sin^m(x^n)/x^p\,\mathrm dx$

Why is $\int_{-\infty}^\infty \frac{1}{\sinh^2(t-i)} dt = -2$?

Formula for a sequence defined on $K_1(x,y) := y+0$ if $x \geq y$ and $y-1$ otherwise