Category: Integration

Question Number 63410 by aliesam last updated on 03/Jul/19 Commented by mathmax by abdo last updated on 03/Jul/19 $$2)letI=\int \frac{xdx}{1+sinx}changementtan\left(\frac{x}{2}\right)=tgive$$$${I}\:=\:\int\:\:\:\frac{\mathrm{2}{arctan}\left({t}\right)}{\left(\mathrm{1}+\frac{\mathrm{2}{t}}{\mathrm{1}+{t}^{\mathrm{2}} }\right)\left(\mathrm{1}+{t}^{\mathrm{2}} \right)}{dt}\:=\:\mathrm{2}\int\:\:\:\:\frac{{arctan}\left({t}\right)}{\mathrm{1}+{t}^{\mathrm{2}} \:+\mathrm{2}{t}}\:{dt}\:=\mathrm{2}\:\int\:\:\:\frac{{arctan}\left({t}\right)}{\left({t}+\mathrm{1}\right)^{\mathrm{2}} }\:{dt}\:\:…

Question Number 63405 by mathmax by abdo last updated on 03/Jul/19 $$find\int \sqrt{\frac{x^2-4x+1}{x+2}}dx$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 63395 by mathmax by abdo last updated on 03/Jul/19 $$letf\left(t\right)={\int }_0^{\mathrm{\infty }}\frac{ln(1+tx)}{1+x^2}dxwith\mid t\mid <1$$$$1)determineaexplicitformoff\left(t\right)$$$$2)findthevalueof{\int }_0^{\mathrm{\infty }}\frac{ln(1+x)}{1+x^2}dx$$ Commented…

Question Number 128922 by mnjuly1970 last updated on 11/Jan/21 $$\dots advancedcalculus\dots$$$$evaluate:::$$$$\mathrm{\Omega }={\int }_0^{\frac{1}{2}}\frac{\mathrm{Arctanh}\left(x\right)}{x}dx=?$$$$$$ Answered by Dwaipayan Shikari last…

Question Number 128900 by bemath last updated on 11/Jan/21 $$\int \frac{4\mathrm{x}+5}{(\mathrm{x}+2)(\mathrm{x}+3)(\mathrm{x}+4)(\mathrm{x}+5)+1}\mathrm{dx}?$$ Answered by liberty last updated on 11/Jan/21 $$\int \frac{4\mathrm{x}+5}{({\mathrm{x}}^2+7\mathrm{x}+10)({\mathrm{x}}^2+7\mathrm{x}+12)+1}\mathrm{dx}=(\ast )$$$$\:\left(\mathrm{x}^{\mathrm{2}} +\mathrm{7x}+\mathrm{10}\right)\left(\mathrm{x}^{\mathrm{2}}…