Category: Integration

Question Number 93762 by ckkim89 last updated on 14/May/20 Answered by maths mind last updated on 14/May/20 $$=\frac{4{xe}^{2x}}{4{(1+2x)}^2}=\frac{1}{4}.\frac{{de}^{2x}.(1+2x)-d(1+2x).e^{2x}}{{(1+2x)}^2}$$$$\Rightarrow\int\frac{{xe}^{\mathrm{2}{x}}…

Question Number 28200 by abdo imad last updated on 21/Jan/18 $$letgiveI={\int }_0^1\frac{ln(1+x)}{1+x^2}dxandJ=\int {\int }_{{[0,1]}^2}\frac{x}{(1+x^2)(1+xy)}dxdy$$$$calculateJbytwomethodsthenfindthevalueofI.$$ Commented by abdo imad…

Question Number 93720 by john santu last updated on 14/May/20 $$\int \frac{\mathit{d}\mathit{x}}{{(\mathit{x}+1)}^3\sqrt{{\mathit{x}}^2+2\mathit{x}}}$$ Commented by john santu last updated on 14/May/20 $$\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{2}\boldsymbol{{x}}\:=\:\boldsymbol{{t}}^{\mathrm{2}\:}…

Question Number 159233 by mnjuly1970 last updated on 14/Nov/21 Answered by mindispower last updated on 16/Nov/21 $$A_{2n}=\sum _{k⩾1}\frac{1}{{\left(2k\right)}^{2n}}=\frac{1}{2^{2n}}.\zeta \left(2n\right)$$$$\frac{\frac{\zeta\left(\mathrm{2}{n}\right)}{\mathrm{2}^{\mathrm{2}{n}} }}{\mathrm{2}{n}\left(\mathrm{2}{n}+\mathrm{1}\right)}=−\frac{\zeta\left(\mathrm{2}{n}\right)}{\mathrm{2}^{\mathrm{2}{n}} \left(\mathrm{2}{n}+\mathrm{1}\right)}+\frac{\zeta\left(\mathrm{2}{n}\right)}{\mathrm{2}^{\mathrm{2}{n}}…

Question Number 28160 by abdo imad last updated on 21/Jan/18 $$find\int {\int }_D\sqrt{xy}dxdywithD=\{(x,y)\in R^{}/{(x^2+y^2)}^2⩽xy\}$$ Commented by abdo imad last updated on…