Category: Integration

Question Number 98463 by pranesh last updated on 14/Jun/20 Answered by maths mind last updated on 15/Jun/20 $$\underset{k=1}{\sum ^{99}}\frac{x^k}{k}=\int \frac{1-x^{99}}{1-x}dx$$$$\left({cot}\left({x}\right)+……+\frac{{cot}^{\mathrm{99}} \left({x}\right)}{\mathrm{99}}\right)+\int\left(\mathrm{1}+{cot}\left({x}\right)\right)\left(\mathrm{1}+{cot}^{\mathrm{99}}…

Question Number 98445 by mathmax by abdo last updated on 14/Jun/20 $$\mathrm{give}\mathrm{at}\mathrm{form}\mathrm{of}\mathrm{serie}{\mathrm{U}}_{\mathrm{n}}={\int }_0^1\frac{{\mathrm{x}}^{\mathrm{n}}\ln \left(\mathrm{x}\right)}{{(1+\mathrm{x})}^2}\mathrm{dx}$$ Answered by mathmax by abdo last…

Question Number 98426 by mathmax by abdo last updated on 13/Jun/20 $$\mathrm{let}\mathrm{f}\left(\mathrm{x}\right)={\int }_{\frac{\pi }{4}}^{\frac{\pi }{3}}\frac{\mathrm{dt}}{\mathrm{x}+\mathrm{tant}}\mathrm{calculate}\mathrm{f}\left(\mathrm{x}\right)$$$$2)\mathrm{explicit}\mathrm{g}\left(\mathrm{x}\right)={\int }_{\frac{\pi }{4}}^{\frac{\pi }{3}}\frac{\mathrm{dt}}{{(\mathrm{x}+\mathrm{tant})}^2}$$$$\left.\mathrm{3}\right)\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{integrals}\:\int_{\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{3}}} \:\frac{\mathrm{dt}}{\mathrm{2}+\mathrm{tant}}\:\mathrm{and}\:\int_{\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{3}}} \:\frac{\mathrm{dt}}{\left(\mathrm{2}+\mathrm{tant}\right)^{\mathrm{2}}…

Question Number 163954 by mnjuly1970 last updated on 12/Jan/22 Answered by mathmax by abdo last updated on 13/Jan/22 $$\Psi=\mathrm{2}\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{x}^{\mathrm{2}} \:\mathrm{e}^{\mathrm{x}} }{\mathrm{sh}\left(\mathrm{2x}\right)}\mathrm{dx}\:=_{\mathrm{2x}=\mathrm{t}} \:\:\mathrm{2}\int_{\mathrm{0}} ^{\infty}…

Question Number 98338 by  M±th+et+s last updated on 13/Jun/20 $$\int cos\left(x^{18}\right)dx$$$$$$ Answered by smridha last updated on 13/Jun/20 $$\boldsymbol{{let}}\:\boldsymbol{{x}}=\boldsymbol{{k}}^{\frac{\mathrm{1}}{\mathrm{18}}} \boldsymbol{{so}} \…