x-2-cos-x-2-dx-

Question Number 141333 by cesarL last updated on 17/May/21

\int x^{2} \cos (\frac{x}{2}) d x

Answered by qaz last updated on 17/May/21

\int x^{2} \cos \frac{x}{2} d x

= 2 x^{2} \sin \frac{x}{2} - 4 \int x \sin \frac{x}{2} d x

= 2 x^{2} \sin \frac{x}{2} - 4 (- 2 x \cos \frac{x}{2} + 2 \int \cos \frac{x}{2} d x)

= 2 x^{2} \sin \frac{x}{2} + 8 x \cos \frac{x}{2} - 16 \sin \frac{x}{2} + C

Commented by cesarL last updated on 17/May/21

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