Category: Integration

Question Number 216715 by Nadirhashim last updated on 16/Feb/25 $$\mathit{F}ind\int \frac{\mathit{S}in\left(\frac{5x}{2}\right)}{\mathit{S}in\left(\frac{x}{2}\right)}.\mathit{d}\mathit{x}$$ Answered by Frix last updated on 16/Feb/25 $$\int \frac{\sin \frac{5x}{2}}{\sin \frac{x}{2}}dx=\int (2\cos 2x+2\cos x+1)dx=$$$$=\sin 2x+2\sin x+x+C$$ Answered…

Question Number 216613 by ajfour last updated on 12/Feb/25 $${\int }_a^x\frac{1-b\ln \frac{x}{a}}{\sqrt{1-{(1-b\ln \frac{x}{a})}^2}}dx$$ Commented by ajfour last updated on 12/Feb/25 https://youtu.be/Kq4VqD0azog?si=K_P6MADAgm8CXegJ Terms of…

Question Number 216491 by Jubr last updated on 09/Feb/25 Answered by MrGaster last updated on 09/Feb/25 $$\left(1\right):$$$$=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{x}\int_{\mathrm{0}} ^{{x}} \left(\mathrm{1}−{t}^{\mathrm{2}} +\frac{{t}^{\mathrm{4}} }{\mathrm{2}!}−\frac{{t}^{\mathrm{6}} }{\mathrm{3}!}+\ldots\right){dt}}{\:\sqrt{\mathrm{1}−{e}^{−{x}^{\mathrm{2}}…

Question Number 216408 by MrGaster last updated on 07/Feb/25 $${\int }_{-1}^1\frac{1}{x}\sqrt{\frac{1+x}{1-x}}\ln \left(\frac{2x^2+2x+1}{2x^2-2x+1}\right)dx$$ Commented by MrGaster last updated on 07/Feb/25 $${I}=\int_{−\mathrm{1}} ^{+\mathrm{1}}…

Question Number 216372 by glory86 last updated on 06/Feb/25 $$\int \frac{{xe}^x}{{(x+1)}^2}dx$$ Answered by MrGaster last updated on 06/Feb/25 $$\mathrm{Let}u=x+1\Rightarrow du=dx,x=u-1$$$$\int\frac{\left({u}−\mathrm{1}\right){e}^{{u}−\mathrm{1}} }{{u}^{\mathrm{2}}…