Category: Integration

Question Number 18396 by Joel577 last updated on 20/Jul/17 $$\int \sqrt{1+\frac{1}{x^2}+\frac{1}{{(x+1)}^2}}dx$$ Answered by b.e.h.i.8.3.417@gmail.com last updated on 20/Jul/17 $$\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{2}} }+\frac{\mathrm{1}}{\left({x}+\mathrm{1}\right)^{\mathrm{2}} }=\frac{\left({x}^{\mathrm{2}} +{x}\right)^{\mathrm{2}}…

Question Number 83923 by jagoll last updated on 08/Mar/20 $$\int \frac{{\mathrm{x}}^2+20}{{(\mathrm{xsin}\mathrm{x}+5\cos \mathrm{x})}^2}\mathrm{dx}=?$$ Answered by john santu last updated on 08/Mar/20 $$\Rightarrow\mathrm{xsin}\:\mathrm{x}+\mathrm{5cos}\:\mathrm{x}\:=\:\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{25}}\:\mathrm{cos}\:\left(\mathrm{x}−\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{x}}{\mathrm{5}}\right)\right)…

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} \…