Category: Integration

Question Number 203964 by mnjuly1970 last updated on 03/Feb/24 $$$$$$Advancedcalculus\dots$$$$Q:If,{\int }_0^1{\int }_0^1\frac{x\ln \left(x\right){\ln }^2\left(y\right)}{1-xy}dxdy=\lambda \underset{n=1}{\sum ^{\mathrm{\infty }}}\frac{1}{n^3{(n+1)}^2}$$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:\:{Find}\:,\:\:\:\:\:\lambda\:=?…

Question Number 203867 by Mathspace last updated on 30/Jan/24 $$find\int \sqrt{\frac{1-x^3}{1+x^3}}dx$$ Answered by MathematicalUser2357 last updated on 06/Feb/24 $$\frac{\mathrm{8}{x}\sqrt{\frac{\mathrm{1}−{x}^{\mathrm{3}} }{{x}^{\mathrm{3}} +\mathrm{1}}}{F}_{\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{3}};−\frac{\mathrm{1}}{\mathrm{2}},\frac{\mathrm{1}}{\mathrm{2}};\frac{\mathrm{4}}{\mathrm{3}};{x}^{\mathrm{3}}…

Question Number 203772 by Calculusboy last updated on 27/Jan/24 Answered by witcher3 last updated on 27/Jan/24 $$\mathrm{no}\mathrm{close}\mathrm{formes}\mathrm{just}\mathrm{series}\mathrm{or}\mathrm{aproximination}$$ Commented by Calculusboy last updated on…

Question Number 203714 by K1000 last updated on 26/Jan/24 $$\int 2x^2$$ Answered by Frix last updated on 26/Jan/24 $$\int {ax}^{n}dx=a\int x^{n}dx=\frac{{ax}^{n+1}}{n+1}+C$$…

Question Number 203564 by mnjuly1970 last updated on 22/Jan/24 $$$$$${\int }_0^{\mathrm{\infty }}\frac{{sin}^3\left(x\right)}{x^2}dx=?$$ Answered by Mathspace last updated on 23/Jan/24…