Category: Integration

Question Number 187602 by horsebrand11 last updated on 19/Feb/23 $$\underset{1/4}{\stackrel{1/2}{\int }}\frac{{\sin }^{-1}\left(\sqrt{x}\right)-{\cos }^{-1}\left(\sqrt{x}\right)}{{\sin }^{-1}\left(\sqrt{x}\right)+{\cos }^{-1}\left(\sqrt{x}\right)}dx=?$$ Answered by integralmagic last updated on 19/Feb/23…

Question Number 122044 by rs4089 last updated on 13/Nov/20 Commented by JDamian last updated on 13/Nov/20 $$\mathrm{What}\mathrm{is}{C}_r?$$ Commented by rs4089 last updated…

Question Number 187529 by sciencestudentW last updated on 18/Feb/23 $$\int x^2\cdot {sin}^{-1}\left(x\right)dx=?$$ Answered by Humble last updated on 18/Feb/23 $$\int {\mathit{x}}^2\mathit{a}\mathit{r}\mathit{c}\mathit{s}\mathit{i}\mathit{n}\left(\mathit{x}\right)\mathit{d}\mathit{x}$$$$\boldsymbol{{I}}{BP}…

Question Number 187528 by sciencestudentW last updated on 18/Feb/23 $$\underset{\frac{9\pi }{2}}{\stackrel{\frac{7\pi }{1.5}}{\int }}\frac{dx}{\sqrt{1-sinx}}=?$$ Answered by ARUNG_Brandon_MBU last updated on 18/Feb/23 $$I=\int \frac{dx}{\sqrt{1-\sin x}}$$$$\:\:=\int\frac{{dx}}{\mid\mathrm{cos}\frac{{x}}{\mathrm{2}}−\mathrm{sin}\frac{{x}}{\mathrm{2}}\mid}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\int\frac{{dx}}{\mathrm{cos}\left(\frac{{x}}{\mathrm{2}}+\frac{\pi}{\mathrm{4}}\right)} \…

Question Number 187526 by sciencestudentW last updated on 18/Feb/23 $$\int \frac{dx}{cscx-1}=?$$ Answered by ARUNG_Brandon_MBU last updated on 18/Feb/23 $$I=\int \frac{dx}{\mathrm{cosec}x-1}$$$$=\int \frac{\sin x}{1-\sin x}dx=\int (\frac{1}{1-\sin x}-1)dx$$$$\:\:=\int\frac{\mathrm{1}+\mathrm{sin}{x}}{\mathrm{cos}^{\mathrm{2}} {x}}{dx}−{x}=\mathrm{tan}{x}+\frac{\mathrm{1}}{\mathrm{cos}{x}}−{x}+{C}…