I have to integrate $\displaystyle \int_{0}^{\pi}x \sin^{2}x \cos x dx$ using reduction formula. I am know that for using reduction formula i have to convert my limit in $0$ to $\displaystyle \frac{\pi}{2}$, for that i using the formula that $\displaystyle \sin^{2}x= 4\sin^{2}\frac{x}{2}\cos^{2}\frac{x}{2}$ and $\displaystyle \cos x=2\cos^{2}\frac{x}{2}+1$ and then i am taking $\displaystyle \frac{x}{2}=t$ after that i am stuck. So please help me to get answer.
To integrate: $\int_{0}^{\pi}x\sin ^{2}x \cos x dx$
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integration
definite-integrals
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0I am thinking let $t=\tan(x/2)$. – 2012-10-14
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0If i take $\displaystyle x=\pi$ then $t=\infty$ so how can i use reduction formula? – 2012-10-14