Category: Integration

Question Number 137693 by Mathspace last updated on 05/Apr/21 $$calculate{\int }_0^{\mathrm{\infty }}\frac{cos\left(sinx\right)-sin\left(cosx\right)}{x^2+8}dx$$ Answered by mathmax by abdo last updated on 07/Apr/21 $$\int_{\mathrm{0}}…

Question Number 137668 by mnjuly1970 last updated on 05/Apr/21 $$\dots \dots .advanced\dots \dots \dots \dots calculus\dots .$$$$provethat:::::\ast \ast \ast \ast \ast$$$$\mathbf{\Omega }=\underset{n=0}{\sum ^{\mathrm{\infty }}}\frac{\mathrm{\Gamma }(n+1)\mathrm{\Gamma }(x+1)}{(n+1)\mathrm{\Gamma }(n+x+2)}={\psi }^{\prime }(x+1)$$$$proof::$$$$\:\:\:\:\Omega=\underset{{n}=\mathrm{0}\:} {\overset{\infty} {\sum}}\frac{\beta\:\left({n}+\mathrm{1},{x}+\mathrm{1}\right)}{{n}+\mathrm{1}}=\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left\{\frac{\mathrm{1}}{\left({n}+\mathrm{1}\right)}\int_{\mathrm{0}} ^{\:\mathrm{1}}…

Question Number 137656 by rs4089 last updated on 05/Apr/21 $${\int }_0^{\mathrm{\infty }}sin\left(x^p\right)dx$$ Answered by Dwaipayan Shikari last updated on 05/Apr/21 $$\int_{\mathrm{0}} ^{\infty}…

Question Number 137605 by mnjuly1970 last updated on 04/Apr/21 $$\dots ..nicecalculus\dots$$$$provethat::$$$$\underset{n=0}{\sum ^{\mathrm{\infty }}}{tan}^{-1}\left(\frac{1}{F_n}\right).{tan}^{-1}\left(\frac{1}{F_{n+1}}\right)=\frac{{\pi }^2}{4}$$$$\:\:{F}_{{n}} \:{is}\:{fibonacci}\:{sequence}…. \…

Question Number 72060 by Tushar rathore last updated on 23/Oct/19 $$\int \frac{\sin x}{1+\sin x+\sin 2x}dx=?$$ Commented by Tushar rathore last updated on 27/Oct/19 $$anyonetriedthis$$ Commented…