Category: Integration

Question Number 178922 by mnjuly1970 last updated on 22/Oct/22 Answered by ARUNG_Brandon_MBU last updated on 22/Oct/22 $$\frac{1}{n(n+1)(n+2)}=\frac{\frac{1}{2}}{n}-\frac{1}{n+1}+\frac{\frac{1}{2}}{n+2}$$$${\left(\frac{1}{n(n+1)(n+2)}\right)}^2=\frac{1}{4}{(\frac{1}{n}-\frac{2}{n+1}+\frac{1}{n+2})}^2$$$$=\frac{\mathrm{1}}{\mathrm{4}}\left(\frac{\mathrm{1}}{{n}^{\mathrm{2}} }+\frac{\mathrm{4}}{\left({n}+\mathrm{1}\right)^{\mathrm{2}} }+\frac{\mathrm{1}}{\left({n}+\mathrm{2}\right)^{\mathrm{2}} }+\mathrm{2}\left(\frac{−\mathrm{2}}{{n}\left({n}+\mathrm{1}\right)}+\frac{−\mathrm{2}}{\left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)}+\frac{\mathrm{1}}{{n}\left({n}+\mathrm{2}\right)}\right)\right)…

Question Number 113323 by AbhishekBasnet last updated on 12/Sep/20 Answered by bemath last updated on 12/Sep/20 $$\mathrm{let}\mathrm{a}+\mathrm{bx}=\mathrm{u},\mathrm{x}=\frac{\mathrm{u}-\mathrm{a}}{\mathrm{b}}$$$$\int \left(\frac{\mathrm{u}-\mathrm{a}}{\mathrm{b}}\right){\mathrm{u}}^3\left(\frac{\mathrm{du}}{\mathrm{b}}\right)=\frac{1}{{\mathrm{b}}^2}\int ({\mathrm{u}}^4-{\mathrm{au}}^3)\mathrm{du}$$$$=\frac{\mathrm{1}}{\mathrm{b}^{\mathrm{2}}…

Question Number 113275 by bemath last updated on 12/Sep/20 $$\int \frac{\mathrm{dx}}{3\sin \mathrm{x}+\sin {}^3\mathrm{x}}?$$ Answered by bemath last updated on 12/Sep/20 $$\mathrm{I}=\int \frac{\mathrm{dx}}{\sin \mathrm{x}(3+\sin {}^2\mathrm{x})}$$$$\mathrm{I}=\int\:\frac{\mathrm{sin}\:\mathrm{x}\:\mathrm{dx}}{\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}\left(\mathrm{3}+\mathrm{sin}\:^{\mathrm{2}}…

Question Number 47720 by maxmathsup by imad last updated on 13/Nov/18 $$find\int ln(1+x^3)dx$$ Answered by MJS last updated on 14/Nov/18 $$\int\mathrm{ln}\:\left({x}^{\mathrm{3}} +\mathrm{1}\right)\:{dx}= \…

Question Number 47677 by vajpaithegrate@gmail.com last updated on 13/Nov/18 $$\int {\mathrm{x}}^{\mathrm{x}}\mathrm{dx}=$$ Commented by maxmathsup by imad last updated on 13/Nov/18 $$atformofserie$$$$\int\:{x}^{{x}}…