Category: Integration

Question Number 36438 by prof Abdo imad last updated on 02/Jun/18 $$letF\left(x\right)={\int }_x^{\frac{1}{x}}\frac{arctan\left(t\right)}{t}dt$$$$1)calculate\frac{dF}{dx}\left(x\right)$$$$2)findF\left(x\right).$$ Commented by tanmay.chaudhury50@gmail.com last updated…

Question Number 167510 by Mathspace last updated on 18/Mar/22 $$explicitef\left(a\right)={\int }_0^{\frac{\pi }{2}}ln(a+{tan}^{2}x)dx$$$$a⩾2$$ Answered by ArielVyny last updated on 20/Mar/22 $${f}\left({a}\right)=\int_{\mathrm{0}}…

Question Number 36435 by prof Abdo imad last updated on 02/Jun/18 $$findthevalueofh\left(t\right)={\int }_0^{1}ln(1+{tx}^2)with\mid t\mid ⩽1$$$$2)calculate{\int }_0^{1}ln(1+x^2)dx$$$$\left.\mathrm{3}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}−{x}^{\mathrm{2}} \right){dx}…

Question Number 36433 by prof Abdo imad last updated on 02/Jun/18 $$valculatef\left(x\right)={\int }_0^2\frac{{(x+2)}^2}{\sqrt{x^2+4x+5}}dx$$ Commented by abdo.msup.com last updated on 02/Jun/18…

Question Number 36431 by prof Abdo imad last updated on 02/Jun/18 $$calculate{\int }_0^1\frac{x+1}{{(x^2+1)}^2}dx$$ Commented by prof Abdo imad last updated…