Category: Integration

Question Number 45019 by rahul 19 last updated on 07/Oct/18 Answered by tanmay.chaudhury50@gmail.com last updated on 08/Oct/18 $$lett=1+\frac{x}{1!}+\frac{x^2}{2\cdot !}+\frac{x^3}{3!}+\dots +\frac{x^n}{n!}$$$$\frac{{dt}}{{dx}}=\mathrm{0}+\mathrm{1}+\frac{{x}}{\mathrm{1}!}+\frac{{x}^{\mathrm{2}} }{\mathrm{2}!}+..+\frac{{x}^{{n}−\mathrm{1}} }{\left({n}−\mathrm{1}\right)!}+\frac{{x}^{{n}}…

Question Number 110551 by shahria14 last updated on 29/Aug/20 Answered by Dwaipayan Shikari last updated on 29/Aug/20 $${\int }_0^{\pi }\frac{x}{1+sinx}dx={\int }_0^{\pi }\frac{\pi -x}{1+sinx}dx=I$$$$\mathrm{2}{I}=\int_{\mathrm{0}} ^{\pi}…

Question Number 110543 by mnjuly1970 last updated on 29/Aug/20 Answered by mathdave last updated on 29/Aug/20 $$solution$$$$lety=x^{2}anddx=\frac{1}{2\sqrt{y}}dythenputtinginto$$$${I}=\frac{\mathrm{1}}{\mathrm{2}}\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{ln}\left(\mathrm{1}−{y}\right)\mathrm{ln}\left(\mathrm{1}+{y}\right)}{{y}}{dy} \…

Question Number 44992 by manish09@gmail.com last updated on 07/Oct/18 $$\int {\mathrm{e}}^{\mathrm{x}}\left(\frac{1-\sin \mathrm{x}}{1+\cos \mathrm{x}}\right)\mathrm{dx}?$$ Answered by tanmay.chaudhury50@gmail.com last updated on 07/Oct/18 $$\int e^x\left(\frac{1-2sin\frac{x}{2}cos\frac{x}{2}}{2{cos}^2\frac{x}{2}}\right)$$$$\int{e}^{{x}}…

Question Number 44921 by manish09@gmail.com last updated on 06/Oct/18 $$\int \frac{1}{1+\ln \mathrm{x}}=?$$ Commented by MJS last updated on 06/Oct/18 $$\mathrm{see}\mathrm{question}44674$$ Answered by tanmay.chaudhury50@gmail.com…