New posts in definite-integrals

Solving the integral $\int_0^1\int_0^1\frac{1}{(1-\alpha x^\beta y^\gamma)^2}dxdy$

integration definite-integrals

Prove $ \int_{5\pi/36}^{7\pi/36} \ln (\cot t )dt +\int_{\pi/36}^{3\pi/36} \ln (\cot t )dt = \frac49G $

real-analysis calculus integration definite-integrals catalans-constant

Area under the graph and Integrals

calculus definite-integrals

Prove that $\int_0^\infty \frac{e^{\cos(ax)}\cos\left(\sin (ax)+bx\right)}{c^2+x^2}dx =\frac{\pi}{2c}\exp\left(e^{-ac}-bc\right)$

calculus real-analysis integration definite-integrals improper-integrals

How can I show that $ \int_0^\pi \frac{x\,dx}{1+\cos^2(x)} = \frac{\pi^2}{2\sqrt{2}} $

calculus integration definite-integrals

Strategies for evaluating sums $\sum_{n=1}^\infty \frac{H_n^{(m)}z^n}{n}$

sequences-and-series definite-integrals closed-form harmonic-numbers polylogarithm

Evaluate $ \lim_{x \to \infty} e^{-x^2} \int_x^{x + \ln(x)/x} e^{-t^2} dt $

calculus limits definite-integrals

Evaluating $\int_0^{\infty} \log(\sin^2(x))\left(1-x\operatorname{arccot}(x)\right) \ dx$

calculus real-analysis integration definite-integrals

Help with $-\int_0^1 \ln(1+x)\ln(1-x)dx$

sequences-and-series definite-integrals digamma-function

Prove that $\int_{0}^{\infty}\frac{(\arctan x)^3}{x^3}dx=\frac{3π}{2}\ln2-\frac{π^3}{16}$

calculus integration definite-integrals

Solve $\int_0^{2\pi} \cos(a\cos(x) + b\sin(x) + cx + d)dx$

integration definite-integrals bessel-functions

How to find $\int_{-1}^1 \frac{\cos x}{a^x+1}\mathrm dx$

calculus integration definite-integrals

Evaluate $\int\limits_0^{\frac{\pi}{2}} \frac{\sin(2nx)\sin(x)}{\cos(x)}\, dx$

calculus trigonometry integration definite-integrals

Evaluating $\iint_S \sqrt{1+4x^2}\, dS$

definite-integrals

Does order of integration matter, while integrating over a cone?

integration multivariable-calculus definite-integrals multiple-integral cylindrical-coordinates

Taking an integral of an integrand consisting of different power radical functions

calculus integration definite-integrals radicals

Evaluate $\int_0^\infty \frac{e^{-x}}{x}\ln\big(\frac{1}{x}\big) \sin(x)dx$ [closed]

calculus integration complex-analysis definite-integrals

How to calculate $\int_0^{\pi/2} \sin^a x \cos^b x \,\mathrm{d} x$

calculus integration definite-integrals

Unusual integral

definite-integrals improper-integrals euler-mascheroni-constant

Evaluating $\int_1^3\frac{\ln(x+2)}{x^2+2x+15} \ dx$

calculus integration definite-integrals