Category: Integration

Question Number 83917 by turbo msup by abdo last updated on 07/Mar/20 $$find\int \frac{dx}{{(1+\sqrt{1+x^2})}^2}$$ Answered by redmiiuser last updated on 08/Mar/20 Answered…

Question Number 83899 by john santu last updated on 07/Mar/20 $$\mathrm{Defined}\mathrm{a}\mathrm{function}\mathrm{f}\left(\mathrm{x}\right)\mathrm{such}$$$$\mathrm{that}\mathrm{f}(1-\mathrm{x})+2\mathrm{f}\left(\mathrm{x}\right)=\mathrm{nx}$$$$\mathrm{for}\mathrm{m},\mathrm{n}>1,\mathrm{the}\mathrm{value}\mathrm{of}$$$$\int \underset{1}{\stackrel{\mathrm{m}}{}}(2\mathrm{n}+6\mathrm{f}\left(\frac{\mathrm{m}}{\mathrm{x}}\right))\mathrm{dx}\mathrm{is}\dots$$ Commented by john santu…

Question Number 83893 by sahnaz last updated on 07/Mar/20 $$\int \frac{\mathrm{du}}{\mathrm{u}-{\mathrm{u}}^2}$$ Commented by abdomathmax last updated on 07/Mar/20 $$\int \frac{du}{u-u^2}=\int \frac{du}{u(1-u)}=\int (\frac{1}{u}+\frac{1}{1-u})du$$$$={ln}\mid\frac{{u}}{\mathrm{1}−{u}}\mid\:+{C} \…

Question Number 83852 by M±th+et£s last updated on 06/Mar/20 $$f\left(\alpha \right)={\int }_0^{\mathrm{\infty }}\frac{e^{-\alpha x}sin\left(x\right)}{x}dx$$ Commented by mathmax by abdo last updated on 06/Mar/20 $${for}\:\alpha\geqslant\mathrm{0}\:\:{we}\:{have}\:{f}^{'}…

Question Number 83842 by M±th+et£s last updated on 06/Mar/20 $$\int \frac{ln\left(x\right)}{ln(6x-x^2)}dx$$ Commented by Henri Boucatchou last updated on 06/Mar/20 $${Using}\:\:\:\frac{{lnA}}{{lnB}}=\frac{{A}}{{B}},\:\:\:\:\:\:\:\:\int\frac{{x}}{\mathrm{6}{x}−{x}^{\mathrm{2}} }{dx}=\int\left(−\frac{\mathrm{1}}{\mathrm{2}}\frac{\mathrm{2}{x}}{\mathrm{6}−{x}^{\mathrm{2}} }\right){dx}=−\frac{\mathrm{1}}{\mathrm{2}}{ln}\mid\mathrm{6}−{x}^{\mathrm{2}} \mid\:+\:{Cte}…