New posts in Definite Integrals

Definite integral evaluation of $\frac{\sin^2 x}{2^x + 1}$

Evaluating $\sum _{k=1}^{\infty }\frac{H_k}{4^k\left(2k+1\right)}\binom{2k}{k}$.

Why does 'The King Property' of integration work?

Challenging problem: Calculate $\int_0^{2\pi}x^2 \cos(x)\operatorname{Li}_2(\cos(x))dx$

Approximating $\int_1^\infty x^a (x-1)^b e^{cx}dx$

Compute the limit $\lim\limits_{t \to + \infty} \int_0^{+ \infty} \frac{ \mathrm d x}{e^x+ \sin tx} $

Evaluating $\int_{0}^{\pi}\ln (1+b\cos x)\ \text{d}x$, $b$ is a parameter

Integral $\int_0^y \exp\left( \alpha x + \frac{1}{1-\beta e^{\gamma x}}-\frac{1/\beta }{ 1-\beta e^{-\gamma x}}\right)dx$

Find $\lim_{n\to\infty} n\int_1^e x^a(\log_ex)^ndx$

Prove $\int_0^{\infty }\frac1{\sqrt{x}}\left(\frac{\cos(\pi x^2)}{\sinh (\pi x)}-\frac1{\pi x}\right)dx=\frac{1}{\sqrt{2}}\zeta(\frac{1}{2})$