Integral of $\sin(x)\cdot x^n$
35319
I'm looking for several ways to prove that $\int_{0}^{\infty }\sin(x)x^mdx=\cos(\frac{\pi m}{2})\Gamma (m+1)$
38005
Integral of $\sin (x^3)dx$
828
Computing the integral of $\log(\sin x)$
98933
Calculating the sum of $f(x) = \sum_{n=0}^{\infty} {n \cdot 2^n \cdot x^n}$
105487
Prove that $\sin x \cdot \sin (2x) \cdot \sin(3x) < \tfrac{9}{16}$ for all $x$
51837
Show that $\int_{0}^{\pi} xf(\sin(x))\text{d}x = \frac{\pi}{2}\int_{0}^{\pi}f(\sin(x))\text{d}x$
87169
Convergence of $\int_{1}^{\infty}x\cdot \sin{(e^x})\,dx$
7727
Convergence of series $\sum_{n=1}^\infty\sin(n)\cdot\sin(1/n)$
80553
Show that,$\int_0^\pi \left|\frac{\sin nx}{x}\right|\mathrm{d}x \ge \frac{2}{\pi}\left(1+\frac12+\cdots+\frac{1}{n}\right)$
109901
Computing $\int_0^\infty\frac1{(x+1)(x+2)\cdots(x+n)}\mathrm dx $
42424
Riemann sum of $\sin(x)$
99457
How to integrate $\int x\sin {(\sqrt{x})}\, dx$
25797
Integral of $ x \ln( \sin (x))$ from 0 to $ \pi $
95933
How to evaluate the integral $\int_0^{\pi}\frac{a^n\sin^2x+b^n\cos^2x}{a^{2n}\sin^2x+b^{2n}\cos^2x}dx$?
138914
Reduction formula for $\int \tan^n x dx$
109385
Evaluating the integral $\int_{-\ln 2}^{\ln 2} e^{-x}(\sin x+x)^{1/3}dx$
80319
Integrate: $\int (x^2+a^2)^{-3/2} \cdot dx$