Category: Integration

Question Number 54529 by tarun kunar last updated on 05/Feb/19 $$\int 5\cos x-4\sin x/2\cos x+\sin xdx$$ Commented by maxmathsup by imad last updated on 05/Feb/19 $$letI=\int \frac{5cosx-4sinx}{2cosx+sinx}dxletusethechangementtan\left(\frac{x}{2}\right)=t\Rightarrow$$$${I}\:=\int\:\:\frac{\frac{\mathrm{5}\left(\mathrm{1}−{t}^{\mathrm{2}}…

Question Number 120059 by A8;15: last updated on 29/Oct/20 Answered by Lordose last updated on 29/Oct/20 $$$$$$\mathrm{Firstly},\mathrm{compute}\mathrm{the}\mathrm{indefinite}\mathrm{integral}$$$$\mathrm{I}=\int \mathrm{xsec}\left(2\mathrm{x}\right)\mathrm{dx}=\frac{1}{4}\int \mathrm{asec}\left(\mathrm{a}\right)\mathrm{da}\{\mathrm{a}=2\mathrm{x}\}$$$$\mathrm{I}=\frac{1}{4}(\mathrm{alntan}(\frac{\mathrm{a}}{2}+\frac{\pi }{4})-\int \mathrm{lntan}(\frac{\mathrm{a}}{2}+\frac{\pi }{4})\mathrm{da})\left\{\mathrm{IBP}\right\}$$$$\mathrm{set}\:\frac{\mathrm{a}}{\mathrm{2}}\:+\:\frac{\pi}{\mathrm{4}}\:=\:\mathrm{y}\:\Rightarrow\:\mathrm{da}=\mathrm{2dy}…

Question Number 120025 by mathmax by abdo last updated on 28/Oct/20 $$\mathrm{calculate}{\mathrm{f}}^{{}^{\prime }}\left(\mathrm{x}\right)$$$$1)\mathrm{f}\left(\mathrm{x}\right)={\int }_0^{\mathrm{\infty }}\frac{\cos \left(\mathrm{xt}\right)}{{\mathrm{t}}^2+{\mathrm{x}}^2}\mathrm{dt}$$$$\left.\mathrm{2}\right)\mathrm{f}\left(\mathrm{x}\right)=\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{sin}\left(\mathrm{xt}^{\mathrm{2}} +\sqrt{\mathrm{2}}\right)}{\mathrm{t}^{\mathrm{2}} +\mathrm{x}^{\mathrm{2}}…

Question Number 119970 by bramlexs22 last updated on 28/Oct/20 $$\int \frac{dx}{x^2\sqrt{25-x^2}}?$$ Answered by bemath last updated on 28/Oct/20 $$\:\int\:\frac{{dx}}{{x}^{\mathrm{3}} \sqrt{\frac{\mathrm{25}}{{x}^{\mathrm{2}} }−\mathrm{1}}}\:{dx}\:=\:\int\:\frac{{x}^{−\mathrm{3}} }{\:\sqrt{\mathrm{25}{x}^{−\mathrm{2}}…

Question Number 54416 by 951172235v last updated on 03/Feb/19 Terms of Service Privacy Policy Contact: info@tinkutara.com