Category: Integration

Question Number 87556 by M±th+et£s last updated on 05/Apr/20 Commented by jagoll last updated on 05/Apr/20 $${\mathrm{x}}^3-{2\mathrm{x}}^2+7\mathrm{x}-1=\mathrm{a}{(\mathrm{x}-2)}^2+$$$$\mathrm{b}\left(\mathrm{x}−\mathrm{3}\right)\left(\mathrm{x}−\mathrm{2}\right)^{\mathrm{2}} +\mathrm{c}\left(\mathrm{x}−\mathrm{3}\right)^{\mathrm{2}} \left(\mathrm{x}−\mathrm{2}\right)^{\mathrm{2}} +…

Question Number 87538 by Power last updated on 04/Apr/20 Commented by mathmax by abdo last updated on 04/Apr/20 $$I={\int }_{-1}^1{f}^{-1}\left(x\right)dxchangement{f}^{-1}\left(x\right)=tgivex=f\left(t\right)\Rightarrow$$$${dx}\:={f}^{'}…

Question Number 87534 by mathmax by abdo last updated on 04/Apr/20 $$calculate{\int }_0^{\frac{\pi }{4}}\frac{arctan\left(sinx\right)}{sinx}dx$$ Commented by mathmax by abdo last updated on 06/Apr/20…

Question Number 87527 by mathmax by abdo last updated on 04/Apr/20 $$find{\int }_0^{\mathrm{\infty }}\frac{arctan\left(3x\right)}{x^2+x+1}dx$$ Commented by mathmax by abdo last updated on…

Question Number 87511 by M±th+et£s last updated on 04/Apr/20 Answered by TANMAY PANACEA. last updated on 04/Apr/20 $$t=x^3\to \frac{dt}{3}=x^{2}dx$$$$\int_{{ln}\mathrm{3}} ^{{ln}\mathrm{4}} \frac{\mathrm{1}}{\mathrm{3}}×\frac{{sint}}{{sint}+{sin}\left({ln}\mathrm{12}−{t}\right)}{dt}\:={I} \…