Category: Integration

Question Number 146361 by gsk2684 last updated on 13/Jul/21 $$find\int \frac{1}{x^n+1}dxforn\in N$$ Answered by mathmax by abdo last updated on 13/Jul/21 $$\mathrm{z}^{\mathrm{n}} \:+\mathrm{1}=\mathrm{0}\:\Rightarrow\mathrm{z}^{\mathrm{n}} \:=\mathrm{e}^{\left(\mathrm{2k}+\mathrm{1}\right)\mathrm{i}\pi}…

Question Number 80770 by zainal tanjung last updated on 06/Feb/20 $$\int {\mathrm{x}}^2+3\mathrm{x}\mathrm{dx}=..$$ Commented by zainal tanjung last updated on 06/Feb/20 $$\mathrm{you}\mathrm{are}\mathrm{right}.\mathrm{good}.$$…

Question Number 146307 by mnjuly1970 last updated on 12/Jul/21 $$$$$${\mathrm{S}}_n=\underset{k=1}{\sum ^n}\frac{1}{k(k+2)k+4)}$$$${lim}_{n\to \mathrm{\infty }}\left({\mathrm{S}}_n\right)=?$$ Answered by mathmax by…

Question Number 80752 by bagjamath last updated on 06/Feb/20 Commented by john santu last updated on 06/Feb/20 $$x-2010=t$$$$x-2009=t+1$$$$\int_{−\mathrm{1}} ^{\mathrm{0}} \left({t}^{\mathrm{2}} +{t}\right){dt}\:=\:\frac{\mathrm{1}}{\mathrm{3}}{t}^{\mathrm{3}}…

Question Number 146212 by puissant last updated on 12/Jul/21 $$\mathrm{K}=\int \frac{1}{\sqrt{1+{\mathrm{x}}^3}}\mathrm{dx}$$ Answered by Ar Brandon last updated on 12/Jul/21 $$\mathrm{I}=\int\frac{\mathrm{dx}}{\:\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{3}} }}=\int\frac{\mathrm{dx}}{\:\sqrt{\mathrm{1}+\left(\mathrm{x}^{\mathrm{3}/\mathrm{2}} \right)^{\mathrm{2}} }},\:\mathrm{u}=\mathrm{x}^{\mathrm{3}/\mathrm{2}}…