Category: Integration

Question Number 86671 by M±th+et£s last updated on 30/Mar/20 $$\int sin\left(x\right)arcsin\left(x\right)$$ Answered by Rio Michael last updated on 30/Mar/20 $$\mathrm{let}\mathrm{me}\mathrm{give}\mathrm{a}\mathrm{try}.$$$$\int \sin \left(x\right)\arcsin \left(x\right)dx$$$$\mathrm{using}\:\mathrm{the}\:\mathrm{taylor}\:\mathrm{series}\:\mathrm{expansion}\:\mathrm{for}\:\mathrm{sin}\:\left({x}\right)\:\mathrm{arcsin}\:\left({x}\right)\:\mathrm{centred}\:\mathrm{at}\:\mathrm{0}…

Question Number 152201 by mnjuly1970 last updated on 26/Aug/21 $$$$$$\dots \mathrm{Integral}\dots$$$$\mathrm{I}:={\int }_0^{\pi }ln\left(sin\left(x\right)\right).{tan}^{-1}\left(cot\left(x\right)\right)dx\stackrel{?}{=}0$$$$proof::\dots .$$$$\:\:\:\:\:\:\mathrm{I}\::=\:\int_{\mathrm{0}} ^{\:\pi} {ln}\:\left({sin}\left({x}\right)\:\right).\:{tan}^{\:−\mathrm{1}} \left(\:{tan}\left(\frac{\pi}{\mathrm{2}}\:−{x}\:\right)\right){dx}…

Question Number 86646 by Ar Brandon last updated on 30/Mar/20 $${\int }_0^1\frac{\ln (1+\mathrm{x})}{{\mathrm{x}}^2+1}\mathrm{dx}$$$$$$$$$$$$$$ Commented by mathmax…

Question Number 86638 by M±th+et£s last updated on 29/Mar/20 $$I=\int \frac{x^3-2x^2+7x-1}{{(x-3)}^3{(x-2)}^2}dx$$ Answered by MJS last updated on 29/Mar/20 $$\frac{{x}^{\mathrm{3}} −\mathrm{2}{x}^{\mathrm{2}}…

Question Number 152161 by peter frank last updated on 26/Aug/21 $$\int \cos \left(\log \mathrm{x}\right)\mathrm{dx}$$ Answered by Olaf_Thorendsen last updated on 26/Aug/21 $$\mathrm{F}\left(x\right)=\int \cos \left(\log x\right)dx$$$$\mathrm{F}\left({e}^{{u}} \right)\:=\:\int\mathrm{cos}{u}\:{e}^{{u}} {du}…