Category: Integration

Question Number 43517 by Raj Singh last updated on 11/Sep/18 Commented by maxmathsup by imad last updated on 11/Sep/18 $${let}\:{I}\:=\:\int\:\:\frac{{x}^{\mathrm{3}} \:+\mathrm{1}}{{x}^{\mathrm{2}} −\mathrm{5}{x}\:+\mathrm{6}}\:{dx}\:\Rightarrow{I}\:=\:\int\:\:\frac{{x}\left({x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{6}\:\right)+\mathrm{5}{x}^{\mathrm{2}} −\mathrm{6}{x}\:+\mathrm{1}}{{x}^{\mathrm{2}} −\mathrm{5}{x}\:+\mathrm{6}}{dx}…

Question Number 174560 by mnjuly1970 last updated on 04/Aug/22 $$$$$$\mathrm{\Omega }={\int }_0^1\frac{dx}{\sqrt{8+3x-\sqrt{1+(x^2+3x+2)(x^2+7x+12)}}}$$$$$$ Answered by MJS_new last updated…

Question Number 174548 by mnjuly1970 last updated on 03/Aug/22 $$$$$$\mathit{E}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{a}\mathit{t}\mathit{e}.$$$$\mathbf{\Omega }={\int }_0^2\frac{{\mathit{e}}^{\mathit{x}}}{{\mathit{e}}^{1-\mathit{x}}+{\mathit{e}}^{\mathit{x}-1}}\mathit{d}\mathit{x}=?$$$$$$ Answered by…

Question Number 108990 by shahria14 last updated on 20/Aug/20 Answered by bobhans last updated on 20/Aug/20 $$\frac{\mathrm{♭}o\mathrm{♭}hans}{\varsigma ----\varsigma }$$$$setx-1=\mathrm{♭}\to \{\begin{array}{l}x=5\to \mathrm{♭}=4\\ x=1\to \mathrm{♭}=0\end{array};dx=d\mathrm{♭}$$$$\underset{\mathrm{1}} {\overset{\mathrm{5}} {\int}}{f}\left({x}−\mathrm{1}\right){dx}\:=\:\underset{\mathrm{0}} {\overset{\mathrm{4}} {\int}}\:{f}\left(\flat\right)\:{d}\flat\:=\:\mathrm{0}…

Question Number 43418 by Raj Singh last updated on 10/Sep/18 Answered by tanmay.chaudhury50@gmail.com last updated on 10/Sep/18 $$\int \frac{cosxdx}{sinxcosx+1}$$$$\int \frac{2cosx}{2cosxsinx+2}dx$$$$\int \frac{cosx+sinx+cosx-sinx}{1+{(sinx+cosx)}^2}dx$$$$\int\frac{{cosx}−{sinx}}{\mathrm{1}+\left({sinx}+{cosx}\right)^{\mathrm{2}}…