Category: Integration

Question Number 48261 by Abdo msup. last updated on 21/Nov/18 $$letf\left(x\right)={\int }_{\frac{1}{2}}^1\frac{dt}{2+ch\left(xt\right)}$$$$1)findaexplicitformoff\left(x\right)$$$$2)calculateg\left(x\right)={\int }_{\frac{1}{2}}^1\frac{tsh\left(xt\right)}{{(2+ch\left(xt\right))}^2}dt$$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\frac{\mathrm{1}}{\mathrm{2}}} ^{\mathrm{1}} \:\:\:\frac{{dt}}{\mathrm{2}+{ch}\left(\mathrm{3}{t}\right)}\:{and}\:\int_{\frac{\mathrm{1}}{\mathrm{2}}} ^{\mathrm{1}}…

Question Number 48239 by olj55336@awsoo.com last updated on 21/Nov/18 $$$$$$$$$$$$$$q\dots ..\int \frac{dx}{\sin x\cos x+2\cos {}^{2}x},pleasesolve$$$$$$ Commented by maxmathsup by…

Question Number 113760 by gloriousman last updated on 15/Sep/20 $$\int \sqrt{\frac{\mathrm{x}-1}{{\mathrm{x}}^5}}\mathrm{dx}$$ Answered by bemath last updated on 15/Sep/20 $$I=\int \frac{1}{x^2}\sqrt{\frac{x-1}{x}}dx$$$${I}=\:\int\:\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\:\sqrt{\mathrm{1}−\frac{\mathrm{1}}{{x}}}\:{dx}\:…

Question Number 113745 by Algoritm last updated on 15/Sep/20 Answered by MJS_new last updated on 15/Sep/20 $$\frac{2\cos 2x-\cos x}{6-{\cos }^{2}x-4\sin x}=$$$$=-\frac{\cos x}{{\sin }^{2}x-4\sin x+5}+\frac{2({2\cos }^{2}x-1)}{{\sin }^{2}x-4\sin x+5}$$$$…

Question Number 48182 by cesar.marval.larez@gmail.com last updated on 20/Nov/18 Answered by tanmay.chaudhury50@gmail.com last updated on 20/Nov/18 $$1)t=\frac{x^m{y}^n}{{(x+y)}^{m+n}}$$$$lnt=mlnx+nlny-(m+n)ln(x+y)$$$$\frac{\mathrm{1}}{{t}}\frac{{dt}}{{dx}}=\frac{{m}}{{x}}+\frac{{n}}{{y}}×\frac{{dy}}{{dx}}−\frac{{m}+{n}}{{x}+{y}}\left(\mathrm{1}+\frac{{dy}}{{dx}}\right) \…