Category: Integration

Question Number 115781 by bemath last updated on 28/Sep/20 $$\underset{0}{\stackrel{\frac{1}{\sqrt{2}}}{\int }}\frac{x{\sin }^{-1}\left(x^2\right)}{\sqrt{1-x^4}}dx=?$$$$\int 2^{-x}\tanh \left(2^{1-x}\right)dx=?$$ Answered by bobhans last…

Question Number 50219 by cesar.marval.larez@gmail.com last updated on 14/Dec/18 Answered by peter frank last updated on 15/Dec/18 $$allquestionabovelieontheconcept\left(partialfraction\right)$$$$\int \frac{5\mathrm{x}+3}{{\mathrm{x}}^3-2x^2-2\mathrm{x}}=\int \frac{5\mathrm{x}+3}{x(x+1)(x-3)}$$$$\frac{\mathrm{A}}{\mathrm{x}\:}+\frac{\mathrm{B}}{\mathrm{x}−\mathrm{3}\:}+\frac{\mathrm{C}}{\mathrm{x}+\mathrm{1}} \…

Question Number 115725 by Bird last updated on 28/Sep/20 $$calculate{\int }_0^{\mathrm{\infty }}\frac{lnx}{{(x^2+x+2)}^2}dx$$ Answered by mathmax by abdo last updated on 28/Sep/20…

Question Number 50161 by cesar.marval.larez@gmail.com last updated on 14/Dec/18 $$Findthefunctionwhosefirst$$$$derivativeis8-\frac{5}{\sqrt[3]{x^2}}theinitial$$$$conditionsf\left(8\right)=-20$$ Answered by afachri last updated on 14/Dec/18 $${F}\left({x}\right)\:\:=\:\:\int\:{f}'\left({x}\right)\:\:{dx}…

Question Number 115689 by Algoritm last updated on 27/Sep/20 Answered by mathmax by abdo last updated on 27/Sep/20 $$\mathrm{I}={\int }_0^1\frac{\ln (\mathrm{x}+\sqrt{1-{\mathrm{x}}^2})}{\mathrm{x}}\mathrm{dx}\mathrm{changement}\mathrm{x}=\mathrm{sint}\mathrm{give}$$$$\mathrm{I}\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}}…