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New posts in definite-integrals
How to evaluate the integral $\int_0^\infty \frac{x^{a-1}}{1+bx^a} e^{-x} dx$
calculus
integration
definite-integrals
Different way to show $\int_{-\infty}^{\infty}e^{-\frac{\cosh^2(u)}{2x}}\,e^{-\frac{u^2}{2 t}}\,\cos\left(\frac{\pi\,u}{2t }\right)\,\cosh(u)\,du > 0$
definite-integrals
periodic-functions
Frullani integral $\int_0^\infty \frac{\text{csch}(x)-\frac1x}{x} {\rm d}x$
calculus
integration
definite-integrals
contest-math
improper-integrals
Evaluate alternatively $\int_0^{\frac{\pi}{2}}\operatorname{Li}_2\left(\pm\sin^4x\right)dx$
definite-integrals
special-functions
Compute this integral
calculus
real-analysis
integration
sequences-and-series
definite-integrals
Integral of the Von karman equation
calculus
definite-integrals
summation
Help on an integral.
integration
definite-integrals
An interesting integral with log: $\int_{0}^{\pi/2}\ln^2\left(\tan^2\left({x\over 2}\right)\right)\mathrm dx=\frac{\pi^3}2$ [closed]
real-analysis
integration
definite-integrals
closed-form
show $\int_0^{\infty} \frac{x\sin ax}{x^2+t^2}dx = \frac{\pi}{2}e^{-at}$
integration
measure-theory
definite-integrals
How to integrate $f(x) =\exp(-ax-b/x)$?
calculus
integration
definite-integrals
improper-integrals
Area bounded by $\cos x+\cos y=1$
definite-integrals
area
geometric-probability
trigonometric-integrals
Theorem 6.16 in Baby Rudin: $\int_a^b f d \alpha = \sum_{n=1}^\infty c_n f\left(s_n\right)$
real-analysis
integration
analysis
proof-verification
definite-integrals
Area of a mushroom-shaped curve
integration
definite-integrals
recreational-mathematics
Integral $\int_0^\infty \frac{x-\sin x}{x^3(x^2+4)} dx$
integration
proof-verification
definite-integrals
A complex approach to integral of cardinal sine [duplicate]
calculus
integration
complex-analysis
definite-integrals
improper-integrals
Need help with a definite integral $\int_0^{\infty} \frac{x-1}{\sqrt{2^x-1}\ln(2^x-1)}\,dx$ [duplicate]
calculus
integration
definite-integrals
How to find $I=\int_{-4}^4\int_{-3}^3 \int_{-2}^2 \int_{-1}^1 \frac{x_1-x_2+x_3{-}x_4}{x_1+x_2+x_3+x_4} \, dx_1 \, dx_2 \, dx_3 \, dx_4$
integration
definite-integrals
Approximating $\displaystyle \int_{-\infty}^{\infty}\frac{e^{R+i\,u}}{\ln(R+i\,u)}du$
definite-integrals
complex-integration
oscillatory-integral
Family of Generalized Integrals ${I}(a,b,p)=\int_0^{ab} \left( \left\{\frac{x}{a}\right\}-p\right) \left( \left\{\frac{x}{b}\right\}-p\right) \; dx$
real-analysis
calculus
integration
definite-integrals
solution-verification
Evaluate: $\int_0^1 \sqrt{x+\sqrt{x^2+\sqrt{x^3+\cdots}}}\, dx. $
convergence-divergence
definite-integrals
nested-radicals
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