Category: Integration

Question Number 145775 by Engr_Jidda last updated on 08/Jul/21 $$\int \frac{2x+1}{\sqrt{x^2+4x+5}}dx$$ Answered by mathmax by abdo last updated on 08/Jul/21 $$\Upsilon=\int\:\:\frac{\mathrm{2x}+\mathrm{4}−\mathrm{3}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} \:+\mathrm{4x}+\mathrm{5}}}\mathrm{dx}\:=\int\:\:\frac{\mathrm{2x}+\mathrm{4}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} \:+\mathrm{4x}+\mathrm{5}}}\mathrm{dx}−\mathrm{3}\int\:\frac{\mathrm{dx}}{\:\sqrt{\mathrm{x}^{\mathrm{2}}…

Question Number 14688 by tawa tawa last updated on 03/Jun/17 $$\int \frac{1}{{\sin }^2\left(\mathrm{x}\right){\cos }^2\left(\mathrm{x}\right)}\mathrm{dx}$$ Answered by ajfour last updated on 03/Jun/17 $$\int\frac{\mathrm{4}}{\left(\mathrm{2sin}\:{x}\mathrm{cos}\:{x}\right)^{\mathrm{2}} }{dx}\:\:=\mathrm{4}\int\frac{{dx}}{\left(\mathrm{sin}\:\mathrm{2}{x}\right)^{\mathrm{2}} }…

Question Number 14667 by Umar math last updated on 03/Jun/17 Commented by prakash jain last updated on 03/Jun/17 $$\frac{\mathrm{1}}{\left({x}^{\mathrm{3}} −\mathrm{1}\right)^{\mathrm{3}} }=\frac{\mathrm{1}}{\left({x}−\mathrm{1}\right)^{\mathrm{3}} \left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)^{\mathrm{3}} } \…

Question Number 145722 by madwdah last updated on 07/Jul/21 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 145676 by mnjuly1970 last updated on 07/Jul/21 $$\dots advanced\dots \dots calculus\dots$$$$provethat:$$$$\underset{n=1}{\sum ^{\mathrm{\infty }}}\frac{{(-1)}^{n-1}}{n^3\left(\begin{array}{c}2n\\ n\end{array}\right)}=\frac{2}{5}\zeta \left(3\right)$$$$$$ Answered by Kamel…