Category: Integration

Question Number 160645 by tounghoungko last updated on 03/Dec/21 $$\int \sin {}^8\mathrm{x}\mathrm{dx}=?$$ Commented by swamy1234 last updated on 04/Dec/21 good Answered by puissant last…

Question Number 160636 by mnjuly1970 last updated on 03/Dec/21 $$$$$$provethat$$$$$$$${\int }_0^1{\left(\frac{{tanh}^{-1}\left(x\right)}{x}\right)}^2=\zeta \left(2\right)\mathrm{<img\; draggable="false"\; role="img"\; class="emoji"\; alt="◼"\; src="https://s.w.org/images/core/emoji/15.1.0/svg/25fc.svg">}m.n$$$$$$$$ \…

Question Number 29552 by abdo imad last updated on 09/Feb/18 $$find{\int }_0^{\mathrm{\infty }}\frac{\sqrt{x+1}-1}{x(x+1)}dx.$$ Commented by prof Abdo imad last updated on 11/Feb/18 $${let}\:{put}\:{I}\:=\:\int_{\mathrm{0}}…

Question Number 160597 by cortano last updated on 03/Dec/21 $${\int }_0^{\frac{\pi }{2}}\frac{\mathrm{dx}}{2-\cos \mathrm{x}}=?$$ Answered by Mathspace last updated on 03/Dec/21 $${I}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{{dx}}{\mathrm{2}−{cosx}}\:{we}\:{do}\:{the}\:{changement} \…

Question Number 160594 by cortano last updated on 03/Dec/21 $$\int \frac{\mathrm{dx}}{1-\tan {}^2\left(\mathrm{x}\right)}=?$$ Answered by Mathspace last updated on 03/Dec/21 $$w=\int \frac{dx}{1-{tan}^{2}x}wedothechangement$$$${tanx}={t}\:\Rightarrow{w}=\int\:\:\frac{{dt}}{\left(\mathrm{1}+{t}^{\mathrm{2}} \right)\left(\mathrm{1}−{t}^{\mathrm{2}}…