New posts in integration

When is infinite sum bounded by an integral?

inequality integration summation

Integral $\int_{-2}^0 \frac{x}{\sqrt{e^x+(x+2)^2}}dx$ [duplicate]

Integral of $e^{-x^2}\cos(x^2)$ using residues

calculus complex-analysis integration contour-integration

Integrate $\frac{5x^3 +2}{\sqrt{x^3+1}}$

Why do we use only upper half plane to do Residue Integration?

integration residue-calculus complex-integration

How to evaluate $ \int_0^1 {\log x \log(1-x) \log^2(1+x) \over x} \,dx $ [duplicate]

calculus integration

Why should we get rid of indefinite integration?

integration definite-integrals indefinite-integrals

Computing in closed form $\sum_{n=1}^{\infty}\frac{\operatorname{Ci}\left(\frac{3}{4}\zeta(2) \space n\right)}{n^2}$

calculus real-analysis integration sequences-and-series

Convergence of $\int_0^\infty $sin$ (x^p) dx$

real-analysis integration convergence-divergence improper-integrals

Evaluating $\int_{-\infty}^{\infty}\frac{\sin ax-a \sin x}{x^3(x^2+1)} \ dx$ using contour integration

integration complex-analysis contour-integration

Evaluate integral $\int_0^\pi \sin^4\left(x+\sin 3x\right)dx$

calculus integration definite-integrals

Please help me to find the sum $\sum\limits_{n\geq1} \frac{\sin(nx)}{n^2}$

sequences-and-series integration limits

How to prove $\int_0^1\frac{1-x}{(\ln x)(1+x)}\ dx=\ln\left(\frac2{\pi}\right)$?

real-analysis calculus integration sequences-and-series definite-integrals

Evaluate $\int_{0}^{\frac{\pi}{2}}\frac{dx}{\left(\sqrt{\sin x}+\sqrt{\cos x}\right)^2}$

integration trigonometry definite-integrals closed-form

Evaluating $\int_0^\infty \left| \frac{\sin t}{t} \right|^n \, \mathrm{d}t$ for $n = 3, 5, 7, \dots$

real-analysis calculus integration definite-integrals improper-integrals

An interesting binomial summation

integration sequences-and-series summation binomial-coefficients

How would I find the equation of f(x) in terms of x and y?

calculus integration multivariable-calculus definite-integrals

$\mathbf{E}[\max\{X, a\}] \geq \max\{\mathbf{E}[X], a\}$

integration probability-theory

Need a hint to evaluate the indefinite integral $\int\frac{e^x(2-x^2)}{(1-x)\sqrt{1-x^2}}dx$?

calculus integration indefinite-integrals

Show that $\int_0^1 \frac{\ln(1+x)}x\mathrm dx=-\frac12\int_0^1 \frac{\ln x}{1-x}\mathrm dx$ without actually evaluating both integrals

calculus integration definite-integrals logarithms