Category: Integration

Question Number 28035 by abdo imad last updated on 18/Jan/18 $$findthevalueof{\int }_0^{\mathrm{\infty }}x\frac{arctan\left(2x\right)}{{(2+x^2)}^2}dx.$$ Commented by abdo imad last updated on 23/Jan/18…

Question Number 28033 by abdo imad last updated on 18/Jan/18 $$1)findthevalueof{\int }_0^{\mathrm{\infty }}\frac{ln\left(x\right)}{1+x^2}dx$$$$2)findthevalueof{\int }_0^{\mathrm{\infty }}\frac{xln\left(x\right)}{{(1+x^2)}^2}dx.$$ Commented by abdo…

Question Number 159080 by qaz last updated on 12/Nov/21 $$\underset{\mathrm{n}=0}{\sum ^{\mathrm{\infty }}}\frac{1}{\mathrm{n}!({\mathrm{n}}^4+{\mathrm{n}}^2+1)}=?$$ Answered by mindispower last updated on 13/Nov/21 $$=\underset{{n}\geqslant\mathrm{0}} {\sum}\frac{\mathrm{1}}{{n}!\left({n}^{\mathrm{2}}…

Question Number 27999 by abdo imad last updated on 18/Jan/18 $$find{I}_{n,m}={\int }_0^1{x}^n{(1-x)}^{m}dxwith$$$$(n,m)\in N^{{★}^2}andcalculate\sum _{n=0}^{\propto }{I}_{n,m}.$$…

Question Number 27974 by abdo imad last updated on 18/Jan/18 $$letputf\left(t\right)={\int }_0^{\mathrm{\infty }}\frac{e^{-ax}-e^{-bx}}{x^2}{e}^{-{tx}^2}dx$$$$witht⩾0anda>0andb>0$$$$findaintegralformoff\left(t\right).$$ Commented…