Category: Integration

Question Number 39230 by MJS last updated on 04/Jul/18 $$\int \frac{d\alpha }{\sin 2\alpha +\sin 3\alpha +\sin 5\alpha }=?$$ Answered by tanmay.chaudhury50@gmail.com last updated on 04/Jul/18 $$sin2\alpha +sin3\alpha +sin5\alpha$$$$sin2\alpha +sin3\alpha +sin2\alpha cos3\alpha +cos2\alpha sin3\alpha$$$${sin}\mathrm{2}\alpha\left(\mathrm{1}+{cos}\mathrm{3}\alpha\right)+{sin}\mathrm{3}\alpha\left(\mathrm{1}+{cos}\mathrm{2}\alpha\right) \…

Question Number 104732 by Dwaipayan Shikari last updated on 23/Jul/20 $${\int }_0^{1}log\left(tan\theta \right)d\theta$$$$$$$$$$$$$$$$$$ Terms of…

Question Number 104718 by  M±th+et+s last updated on 23/Jul/20 $$\int {tan}^{-1}\left(\frac{a\sqrt{x}+b}{c}\right)dx$$ Answered by Dwaipayan Shikari last updated on 23/Jul/20 $$\int \frac{2c\sqrt{x}}{a}{tan}^{-1}uduu=\frac{a\sqrt{x}+b}{c}\Rightarrow \frac{a}{2c\sqrt{x}}=\frac{du}{dx}$$$$\frac{\mathrm{2}{c}}{{a}}\int\sqrt{{x}}{tan}^{−\mathrm{1}}…

Question Number 39135 by maxmathsup by imad last updated on 02/Jul/18 $$calculateA\left(\lambda \right)={\int }_0^{\lambda }\frac{ln(x+\sqrt{1+x^2)}}{\sqrt{1+x^2}}dx$$$$2)calculate{\int }_0^1\frac{ln(x+\sqrt{1+x^2)}}{\sqrt{1+x^2}}dx$$ Commented…

Question Number 39120 by math khazana by abdo last updated on 02/Jul/18 $$let{A}_n={\int }_1^n\frac{\left[\sqrt{1+x^2}\right]-\left[x\right]}{x^2}dx(nintegr⩾1)$$$$1)calculate{A}_n$$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} \: \…