Category: Integration

Question Number 168477 by infinityaction last updated on 11/Apr/22 Commented by mr W last updated on 11/Apr/22 $$\pi /3>1$$$$\Rightarrow {\cos }^{-1}\left(\pi /3\right)isnotdefined!$$$$questioniswrong!$$…

Question Number 37404 by ajfour last updated on 12/Jun/18 $${\int }_0^{2\pi }\sqrt{a^2+b^2-2ab\cos \theta }d\theta$$$$witha>b>0.$$ Answered by tanmay.chaudhury50@gmail.com last updated on 13/Jun/18…

Question Number 102922 by mohammad17 last updated on 11/Jul/20 $$\int \frac{dx}{x^3+3x-5}?$$ Commented by prakash jain last updated on 11/Jul/20 $$\mathrm{The}\mathrm{approach}\mathrm{you}\mathrm{take}\mathrm{to}\mathrm{solve}$$$$\mathrm{the}\:\mathrm{question} \…

Question Number 168459 by BegamovSirojiddin last updated on 11/Apr/22 Answered by Mathspace last updated on 11/Apr/22 $$I=\int \frac{dx}{{(x^2+x+1)}^{\frac{5}{2}}}$$$$I=\int \frac{dx}{{({(x+\frac{1}{2})}^2+\frac{3}{4})}^{\frac{5}{2}}}(x+\frac{1}{2}=\frac{\sqrt{3}}{2}tant$$$${I}=\int\frac{\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\left(\mathrm{1}+{tan}^{\mathrm{2}}…

Question Number 168446 by amin96 last updated on 10/Apr/22 Answered by Mathspace last updated on 11/Apr/22 $$\mathrm{\Psi }=\frac{1}{2}{\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}\frac{cos\left(nx\right)}{x^2+1}dx$$$$={Re}\left(\frac{\mathrm{1}}{\mathrm{2}}\int_{−\infty} ^{+\infty\:} \frac{{e}^{{inx}} }{{x}^{\mathrm{2}}…