New posts in Improper Integrals

Wish to evaluate $\int_{0}^{1}\frac{x^4-3x^2+2x}{\sin(\pi x)} dx$

Show that $\int^1_0 \frac{\tanh^{-1} x}{x} \ln [(1 + x)^3 (1 - x)] \, dx = 0$

Existence of improper integral.

Let $f:[a,\infty)\rightarrow \mathbb{R}$ be a uniformly continuous function. $\int_{a}^{\infty} f$ converges.Prove that $\lim_{x\to\infty} f(x)=0$

for $p>0$, when does this integration:$\int_0^{\infty} x^pe^{-x^8\sin^2x}dx$ converge?

What's wrong with this proof that $0 = 1$?

Evaluate the definite integral $\int^{\infty }_{0}\frac{x \,dx}{e^{x} -1}$ using contour integration

Integral $\int_0^\infty \frac{|\sin\sqrt{qx}|-|\sin\sqrt{px}|}{x}dx$

Evaluating $\int\limits_0^\infty \mathcal{e}^{-x}\ln^{2}x\,dx$

Prove that $\int_0^\infty e^{-x} \ln x d x = - \gamma $