Category: Integration

Question Number 183706 by cortano1 last updated on 29/Dec/22 $$A=\int \frac{1+\cos {}^{2}x}{1+\sin {}^{4}x}dx$$ Answered by Ar Brandon last updated on 29/Dec/22 $${A}=\int\frac{\mathrm{1}+\mathrm{cos}^{\mathrm{2}} {x}}{\mathrm{1}+\mathrm{sin}^{\mathrm{4}} {x}}{dx}=\int\frac{\mathrm{sec}^{\mathrm{4}}…

Question Number 118145 by bemath last updated on 15/Oct/20 $$\int \frac{dx}{{(x+1)}^2(x^2+1)}?$$ Commented by bobhans last updated on 15/Oct/20 $$\mathrm{Decomposition}\mathrm{fractional}$$$$\:\frac{\mathrm{1}}{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} \left(\mathrm{x}^{\mathrm{2}}…

Question Number 118111 by bemath last updated on 15/Oct/20 $$\underset{0}{\stackrel{\pi /4}{\int }}\frac{{\mathrm{x}}^2}{{(\mathrm{x}\sin \mathrm{x}+\cos \mathrm{x})}^2}\mathrm{dx}=?$$ Answered by Lordose last updated on 15/Oct/20 $$ \…

Question Number 52550 by Tawa1 last updated on 09/Jan/19 $${\int }_0^{\mathrm{\infty }}\frac{\mathrm{x}}{{\mathrm{e}}^{\mathrm{x}}-1}\mathrm{dx}$$ Commented by maxmathsup by imad last updated on 11/Jan/19 $${let}\:{I}\:=\int_{\mathrm{0}}…

Question Number 118081 by bemath last updated on 15/Oct/20 $$\int \mathrm{arc}\cos \left(\frac{\cos \mathrm{x}}{1+2\cos \mathrm{x}}\right)\mathrm{dx}=?$$ Commented by MJS_new last updated on 15/Oct/20 $$\mathrm{seems}\mathrm{impossible}\mathrm{to}\mathrm{solve}$$ Commented by MJS_new…