Question and Answers Forum

All Questions      Topic List

Integration Questions

Previous in All Question      Next in All Question      

Previous in Integration      Next in Integration      

Question Number 111082 by john santu last updated on 02/Sep/20

$$\left[{\int }_0^{\mathrm{\infty }}JSdx\right]$$$$\underset{0}{\stackrel{\frac{\pi }{2}}{\int }}\frac{\sin \left(x\right)(4+\sin {}^2\left(x\right))}{{(4-\sin {}^2\left(x\right))}^2}dx?$$

Commented by mathdave last updated on 02/Sep/20

$$using{king}^{\prime }spropertyitwillkillit$$

Answered by Sarah85 last updated on 02/Sep/20

$$t=\cos x\Rightarrow dx=-\frac{dt}{\sin x}\mathrm{leads}\mathrm{to}$$$$\int \frac{t^2-5}{{(t^2+3)}^2}dt=\int \frac{dt}{t^2+3}-8\int \frac{dt}{{(t^2+3)}^2}=$$$$=-\frac{\arctan \frac{t}{\sqrt{3}}}{3\sqrt{3}}-\frac{4t}{3(t^2+3)}$$$$...$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com