Category: Integration

Question Number 217431 by peter frank last updated on 13/Mar/25 Answered by Frix last updated on 13/Mar/25 $$\mathrm{Simply}\mathrm{by}\mathrm{parts}:$$$$u^{\prime }=\frac{1}{{(x+1)}^2}\to u=-\frac{1}{x+1}$$$${v}={x}\mathrm{e}^{{x}} \:\rightarrow\:{v}'=\left({x}+\mathrm{1}\right)\mathrm{e}^{{x}} \…

Question Number 217408 by Intesar last updated on 13/Mar/25 $$l\int \sin 7xdx$$ Answered by SdC355 last updated on 13/Mar/25 $$-\frac{1}{7}\cos \left(7x\right)+C$$$$\mathrm{because}.$$$$\frac{\mathrm{d}\:\:}{\mathrm{d}{t}}\:\mathrm{cos}\left({t}\right)=−\mathrm{sin}\left({t}\right) \…

Question Number 217356 by SciMaths last updated on 11/Mar/25 Answered by profcedricjunior last updated on 11/Mar/25 $$\boldsymbol{{i}}=\int_{\mathrm{1}} ^{\mathrm{2}} \int_{\boldsymbol{{y}}} ^{\boldsymbol{{y}}^{\mathrm{2}} } \int_{\mathrm{0}} ^{\boldsymbol{{ln}}\left(\boldsymbol{{y}}+\boldsymbol{{z}}\right)} \boldsymbol{{e}}^{\boldsymbol{{x}}} \boldsymbol{{dxdydz}}…

Question Number 217290 by mnjuly1970 last updated on 08/Mar/25 $$$$$${\int }_0^1\frac{{\ln }^2(1-x)}{x^2}dx=?$$$$$$$$$$ Answered by profcedricjunior…

Question Number 217211 by Ghisom last updated on 06/Mar/25 $$\mathrm{a}\mathrm{nice}\mathrm{one}:$$$$\mathrm{prove}\underset{0}{\stackrel{1}{\int }}\sqrt{-\frac{\ln t}{t}}dt=\sqrt{2\pi }$$ Answered by MrGaster last updated on 06/Mar/25 $$\left(\mathrm{1}\right):\int_{\mathrm{0}} ^{\mathrm{1}}…