New posts in integration

Calculate Fourier series of $f(x)=x^2$ , $x \in \ [-\pi,\pi]$

integration fourier-analysis fourier-series

Evaluation of $\int^1_0\frac{x^b-x^a}{\ln x} d x=\ln{{\frac{1+b}{1+a}}}$

integration definite-integrals

Another math contest problem: $\int_0^{\frac{\ln^22}4}\,\frac{\arccos\frac{\exp\sqrt x}{\sqrt2}}{1-\exp\sqrt{4\,x}}dx$

calculus integration trigonometry contest-math closed-form

Fourier transform of a real function is real

real-analysis integration fourier-analysis fourier-transform

Simple equivalent of $\int_0^\infty\frac{dx}{(x+1)(x+2)...(x+n)}$ when $n\to\infty$

integration definite-integrals improper-integrals

Compute $\lim_{n\to\infty}n^4\int_0^1\frac{x^n\ln^3x}{1+x^n}\ln(1-x)\,dx$

calculus real-analysis integration limits convergence-divergence

Closed-form of $\int_0^{\pi/2}\frac{\sin^2x\arctan\left(\cos^2x\right)}{\sin^4x+\cos^4x}\,dx$

calculus integration trigonometry definite-integrals closed-form

Proving $\lim_{n\to \infty}\int_0^\pi\frac{\sin\left(nx\right)}{1+x^2}dx=0 $

calculus integration limits definite-integrals

Solve $\int_{0}^{1} \log(x)\log(1-x) dx$ without convolution

calculus integration definite-integrals logarithms

Complex Conjugate of Integral

calculus integration complex-analysis functional-analysis

Simple integration: $\int_{-1}^1 \frac{1}{x^2} dx$

integration

Integrating:$\int\limits_0 ^ {\infty}e^{-x^2}\ln(x)dx $

integration definite-integrals gaussian-integral euler-mascheroni-constant

Proof that the Integral of a Positive Function is Positive?

integration

How to calculate $\int_{0}^{\pi/2}{\{\tan(x)\}dx}$

integration definite-integrals

Derivative of Integral with variable bounds

integration derivatives

Justification of substitution in finding indefinite integrals

calculus real-analysis integration indefinite-integrals

Show that $\left(\int_0^1 f(x)\,dx\right)^2\leq2\int_0^1x\, f(x)^2\,dx $

real-analysis inequality integration

About a possible Hardy-type inequality for negative exponents

sequences-and-series functional-analysis inequality integration

Changing the values of an integrable function $f:[a,b] \to \mathbb R$ countably infinitely many points not a dense subset of $[a,b]$

real-analysis integration analysis

When a pole lies outside the circle of integration, what does Cauchy integral formula state?

integration complex-analysis contour-integration