Category: Integration

Question Number 84957 by john santu last updated on 17/Mar/20 $$\int {(2-{\mathrm{x}}^2)}^3\mathrm{dx}=$$ Commented by john santu last updated on 17/Mar/20 $$\int\:\left(\mathrm{8}−\mathrm{3}\left(\mathrm{4x}^{\mathrm{2}} \right)+\mathrm{3}\left(\mathrm{2x}^{\mathrm{4}}…

Question Number 84942 by M±th+et£s last updated on 17/Mar/20 $${\int }_0^{x}sinh(x-t)cosh\left(t\right)dt$$ Answered by mind is power last updated on 17/Mar/20 $${sh}\left({x}\right){ch}\left({y}\right)=\frac{\mathrm{1}}{\mathrm{2}}\left\{{sh}\left({x}+{y}\right)+{sh}\left({x}−{y}\right)\right\} \…

Question Number 84879 by sahnaz last updated on 17/Mar/20 $${\mathrm{e}}^{\int \frac{2\mathrm{dx}}{\mathrm{xlnx}}}$$ Commented by jagoll last updated on 17/Mar/20 $$\int \frac{2\mathrm{dx}}{\mathrm{x}\mathrm{lnx}}=\int \frac{2\mathrm{d}\left(\mathrm{lnx}\right)}{\mathrm{lnx}}=\int 2\frac{\mathrm{du}}{\mathrm{u}}$$$$=2\ln \mathrm{u}+\mathrm{c},[\mathrm{u}=\ln \mathrm{x}]$$$$=\:\mathrm{2ln}\left(\mathrm{lnx}\right)\:+\:\mathrm{2lnC}\:=\:\mathrm{2ln}\left(\mathrm{Clnx}\right) \…

Question Number 84843 by M±th+et£s last updated on 16/Mar/20 $$\int \frac{sin\left(7x\right)}{cos\left(3x\right)}dx$$ Commented by jagoll last updated on 17/Mar/20 $$\sin 7\mathrm{x}=\sin (4\mathrm{x}+3\mathrm{x})$$$$=\sin 4\mathrm{x}\cos 3\mathrm{x}+\cos 4\mathrm{x}\sin 3\mathrm{x}$$$$\int\:\frac{\mathrm{sin}\:\mathrm{7x}}{\mathrm{cos}\:\mathrm{3x}}\:\mathrm{dx}\:=\:\int\:\left(\mathrm{sin}\:\mathrm{4x}\:+\:\mathrm{cos}\:\mathrm{4x}\:\mathrm{tan}\:\mathrm{3x}\right)\mathrm{dx} \…

Question Number 150356 by mnjuly1970 last updated on 11/Aug/21 $$solve\dots$$$$\mathrm{I}:={\int }_0^1\frac{\mathrm{Arcsin}\left(\sqrt{x}\right)}{1-x+x^2}dx=?$$ Answered by Lordose last updated on 12/Aug/21 $$…