Category: Integration

Question Number 130214 by Lordose last updated on 23/Jan/21 $$\int \frac{{\mathrm{u}}^2}{{(1+{\mathrm{u}}^2)}^2}\mathrm{du}$$ Answered by liberty last updated on 23/Jan/21 $$\mathrm{J}=\int\:\frac{\left(\mathrm{u}^{\mathrm{2}} +\mathrm{1}\right)−\mathrm{1}}{\left(\mathrm{1}+\mathrm{u}^{\mathrm{2}} \right)^{\mathrm{2}}…

Question Number 130203 by mnjuly1970 last updated on 23/Jan/21 Answered by Dwaipayan Shikari last updated on 23/Jan/21 $$I\left(a\right)-I\left(\beta \right)={\int }_0^1\frac{x^a}{(1+x)logx}-\frac{x^{\beta }}{(1+x)log\left(x\right)}dx$$$${I}'\left({a}\right)−{I}'\left(\beta\right)=\underset{{n}=\mathrm{1}} {\overset{\infty}…

Question Number 64649 by mathmax by abdo last updated on 20/Jul/19 $$calculate{\int }_0^{2\pi }\frac{cos\theta }{5+3cos\theta }d\theta$$ Commented by mathmax by abdo last updated on 20/Jul/19…

Question Number 64635 by mathmax by abdo last updated on 19/Jul/19 $$1)calculatef\left(a\right)={\int }_0^{\mathrm{\infty }}\frac{arctan\left(\alpha x\right)}{1+x^2}dxwith\alpha real$$$$2)findthevalueof{\int }_0^{\mathrm{\infty }}\frac{arctan\left(2x\right)}{1+x^2}dx$$ Commented by mathmax…

Question Number 130158 by benjo_mathlover last updated on 23/Jan/21 $$\mathrm{Find}\mathrm{the}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{segment}\mathrm{of}\mathrm{the}\mathrm{curve}$$$${\mathrm{y}}^2={\mathrm{x}}^3-{\mathrm{x}}^2\mathrm{if}\mathrm{the}\mathrm{line}\mathrm{x}=2\mathrm{is}\mathrm{the}\mathrm{chord}$$$$\mathrm{determining}\mathrm{the}\mathrm{segment}$$ Answered by liberty last updated on…