Category: Integration

Question Number 64745 by mathmax by abdo last updated on 21/Jul/19 $$calculate{\int }_0^1\frac{sin\left(lnx\right)}{lnx}dx$$ Commented by mathmax by abdo last updated on 21/Jul/19…

Question Number 64735 by mmkkmm000m last updated on 20/Jul/19 $$\int tan\theta /1\stackrel{-}{+}sin\theta d\theta$$ Commented by mr W last updated on 21/Jul/19 $$dearsir:$$$${in}\:{Q}\mathrm{64238}\:{i}\:{asked}\:{if}\:{you}\:{could}\:{use} \…

Question Number 64687 by aliesam last updated on 20/Jul/19 Commented by mathmax by abdo last updated on 21/Jul/19 $$letA=\int \frac{e^{\frac{-cos\left(2x\right)}{2}}}{{sin}^{2}x}dx\Rightarrow A=\int \frac{e^{-\frac{cos\left(2x\right)}{2}}}{\frac{1-cos\left(2x\right)}{2}}dx$$$$=\:\mathrm{2}\:\int\:\:\:\frac{{e}^{−\frac{{cos}\left(\mathrm{2}{x}\right)}{\mathrm{2}}} }{\mathrm{1}−{cos}\left(\mathrm{2}{x}\right)}{dx}\:\:\:{changement}\:{cos}\left(\mathrm{2}{x}\right)\:={t}\:{give}\:\mathrm{2}{x}={argch}\left({t}\right)…

Question Number 130214 by Lordose last updated on 23/Jan/21 $$\int \frac{{\mathrm{u}}^2}{{(1+{\mathrm{u}}^2)}^2}\mathrm{du}$$ Answered by liberty last updated on 23/Jan/21 $$\mathrm{J}=\int\:\frac{\left(\mathrm{u}^{\mathrm{2}} +\mathrm{1}\right)−\mathrm{1}}{\left(\mathrm{1}+\mathrm{u}^{\mathrm{2}} \right)^{\mathrm{2}}…

Question Number 130203 by mnjuly1970 last updated on 23/Jan/21 Answered by Dwaipayan Shikari last updated on 23/Jan/21 $$I\left(a\right)-I\left(\beta \right)={\int }_0^1\frac{x^a}{(1+x)logx}-\frac{x^{\beta }}{(1+x)log\left(x\right)}dx$$$${I}'\left({a}\right)−{I}'\left(\beta\right)=\underset{{n}=\mathrm{1}} {\overset{\infty}…