Category: Integration

Question Number 157932 by cortano last updated on 30/Oct/21 $$provethat{\tan }^{-1}\left(\frac{xy}{rz}\right)+{\tan }^{-1}\left(\frac{xz}{ry}\right)+{\tan }^{-1}\left(\frac{yz}{rx}\right)=\frac{\pi }{2}$$ Commented by cortano last updated on 30/Oct/21 $$nosir.onlyitcondition$$…

Question Number 92397 by john santu last updated on 06/May/20 $$\int \frac{1}{x-\sqrt{1-x^2}}dx$$$$[x=\sin w]$$$$\int \frac{\cos \mathrm{w}\mathrm{dw}}{\sin \mathrm{w}-\cos \mathrm{w}}=\int \frac{\mathrm{dw}}{\tan \mathrm{w}-1}$$$$=\int \frac{{\sec }^2\mathrm{w}\mathrm{dw}}{(\tan \mathrm{w}-1){\sec }^2\mathrm{w}}$$$$=\int \frac{\mathrm{du}}{(\mathrm{u}-1)({\mathrm{u}}^2+1)};[\mathrm{u}=\tan \mathrm{w}]$$$$=\:\int\:\frac{\mathrm{du}}{\mathrm{2}\left(\mathrm{u}−\mathrm{1}\right)}−\int\:\frac{\mathrm{u}\:\mathrm{du}\:}{\mathrm{2}\left(\mathrm{u}^{\mathrm{2}}…

Question Number 92337 by Power last updated on 06/May/20 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 157870 by Odhiambojr last updated on 29/Oct/21 $$findtheintegral:$$$$\int \left\{(3x+1)/(x^2+4)\right\}dx$$ Answered by puissant last updated on 29/Oct/21 $$\Omega=\int\:\frac{\mathrm{3}{x}+\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{4}}{dx}\:=\:\int\frac{\mathrm{3}{x}}{{x}^{\mathrm{2}} +\mathrm{4}}{dx}+\int\frac{{dx}}{{x}^{\mathrm{2}}…

Question Number 26781 by shubhabrata04@gmail.com last updated on 29/Dec/17 Commented by prakash jain last updated on 29/Dec/17 $${\int }_0^1(\log (1-x)-\log x)dx$$$$=\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{log}\:\left(\mathrm{1}−{x}\right){dx}−\int_{\mathrm{0}} ^{\mathrm{1}}…