Category: Integration

Question Number 174118 by Mathspace last updated on 25/Jul/22 $$calculate\sum _{n=1}^{\mathrm{\infty }}\frac{{(-1)}^n}{n}byusing$$$$\psi \left(digamma\right)$$ Answered by mnjuly1970 last updated on 25/Jul/22 $$\:\:\:\underset{{n}=\mathrm{1}}…

Question Number 108573 by mnjuly1970 last updated on 17/Aug/20 $$\mathrm{please}:\mathrm{in}\mathrm{A}\stackrel{\mathrm{\Delta }}{\mathrm{B}C}\mathrm{prove}\mathrm{that}:$$$$\frac{cos\left(\mathrm{A}\right)}{sin\left(\mathrm{B}\right)sin\left(\mathrm{C}\right)}+\frac{cos\left(\mathrm{B}\right)}{sin\left(\mathrm{A}\right)sin\left(\mathrm{C}\right)}+\frac{cos\left(\mathrm{C}\right)}{sin\left(\mathrm{A}\right)sin\left(\mathrm{B}\right)}=2$$$$$$$$$$ Answered by veth last updated on…

Question Number 43027 by Raj Singh last updated on 06/Sep/18 Commented by math khazana by abdo last updated on 07/Sep/18 $$letI=\int \frac{x^2+1}{{(x+1)}^3(x-2)}dxletdecompose$$$${F}\left({x}\right)=\frac{{x}^{\mathrm{2}}…

Question Number 42994 by MJS last updated on 06/Sep/18 $$\int \sqrt{1+\frac{\cos x}{4\tan x}}dx=?$$ Commented by tanmay.chaudhury50@gmail.com last updated on 06/Sep/18 $$thisproblemsnatchedthesleepandmindhovering$$$$togettheanswer\dots$$ Commented…

Question Number 108506 by mnjuly1970 last updated on 17/Aug/20 Answered by mathmax by abdo last updated on 17/Aug/20 $$\mathrm{A}\:=\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{ln}\left(\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)}{\mathrm{x}^{\mathrm{2}} \left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{3}\right)}\mathrm{dx}\:\Rightarrow\mathrm{A}\:=_{\mathrm{x}=\sqrt{\mathrm{3}}\mathrm{t}} \:\:\:\int_{\mathrm{0}}…