Newbetuts

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

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

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

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

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

How to find $\int_{0}^{2\pi} \frac{\cos(n\theta)}{(\cos(\theta)+\alpha)^2}d\theta, \alpha>1$

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

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

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

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

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

A double sum or a definite integral.

Applications of Ramanujan's Master Theorem

closed form for $\int_0^{\infty}\log^n\left(\frac{e^x}{e^x-1}\right)dx$

Integrate $\int_0^\infty \frac{dx}{(x^2+2x+12)^2}$ using residues

Show a detail prove of : $\int_{0}^{1}\int_{0}^{1}\left({x\over 1-xy}\cdot{\ln{x}-\ln{y}\over \ln{x}+\ln{y}}\right)\mathrm dx\mathrm dy=1-2\gamma$

$\int_{0}^{1}\frac{\sin^{-1}\sqrt x}{x^2-x+1}dx$

New posts in definite-integrals

Evaluating $\lim_{n \to \infty} \int_{0}^{\pi} \frac{\sin x}{1+\cos ^2(nx)} dx$

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

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

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

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

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

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

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

How to find $\int_{0}^{2\pi} \frac{\cos(n\theta)}{(\cos(\theta)+\alpha)^2}d\theta, \alpha>1$

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

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

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

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

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

A double sum or a definite integral.

Applications of Ramanujan's Master Theorem

closed form for $\int_0^{\infty}\log^n\left(\frac{e^x}{e^x-1}\right)dx$

Integrate $\int_0^\infty \frac{dx}{(x^2+2x+12)^2}$ using residues

Show a detail prove of : $\int_{0}^{1}\int_{0}^{1}\left({x\over 1-xy}\cdot{\ln{x}-\ln{y}\over \ln{x}+\ln{y}}\right)\mathrm dx\mathrm dy=1-2\gamma$

$\int_{0}^{1}\frac{\sin^{-1}\sqrt x}{x^2-x+1}dx$