Category: Integration

Question Number 168812 by infinityaction last updated on 18/Apr/22 $${\int }_0^{\pi }{\left(\sin x\right)}^{\cos x}dx$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 168772 by Dildora last updated on 17/Apr/22 Commented by safojontoshtemirov last updated on 18/Apr/22 $$S=4\underset{0}{\stackrel{\frac{\pi }{2}}{\int }}\sqrt{{\left({\left(e^{t}sint\right)}^{\prime }\right)}^2+{\left({\left(e^{t}cost\right)}^{\prime }\right)}^2}dt$$$${S}=\mathrm{4}\underset{\mathrm{0}}…

Question Number 168762 by Dildora last updated on 17/Apr/22 Commented by cortano1 last updated on 17/Apr/22 $$\int \frac{2\sin \frac{1}{2}x\cos \frac{1}{2}x}{2\cos \frac{1}{2}x(\cos \frac{1}{2}x+\sin \frac{1}{2}x)}dx$$$$=\int \frac{\sin \frac{1}{2}x}{\cos \frac{1}{2}x+\sin \frac{1}{2}x}dx$$$$=\int \frac{2\sin u}{\cos u+\sin u}du;[\frac{1}{2}x=u]$$$$\frac{2\sin u}{\cos u+\sin u}=A\left(\frac{\sin u+\cos u}{\sin u+\cos u}\right)+B\left(\frac{d(\sin u+\cos u)}{\sin u+\cos u}\right)$$$$\Rightarrow\mathrm{2sin}\:{u}=\:{A}\mathrm{sin}\:{u}+{A}\mathrm{cos}\:{u}+{B}\mathrm{cos}\:\:{u}−{B}\mathrm{sin}\:{u}…

Question Number 168745 by MikeH last updated on 17/Apr/22 $$\int \frac{1}{x+\sqrt{x-1}}dx=??$$ Commented by safojontoshtemirov last updated on 17/Apr/22 $$\int \frac{dx}{x+\sqrt{x-1}}=\sqrt{x-1}=t;x=t^2+1;dx=2tdt$$$$\int\frac{\mathrm{2}{tdt}}{{t}^{\mathrm{2}} +{t}+\mathrm{1}}=\int\frac{\mathrm{2}{t}+\mathrm{1}}{{t}^{\mathrm{2}} +{t}+\mathrm{1}}{dt}−\int\frac{\mathrm{1}}{{t}^{\mathrm{2}}…

Question Number 103198 by Dwaipayan Shikari last updated on 13/Jul/20 $${\int }_0^{1}sin\left(logx\right)dx$$ Commented by Dwaipayan Shikari last updated on 13/Jul/20 $${sinx}=\frac{{e}^{{ix}} −{e}^{−{ix}}…