What is the integral of x^2cos(x/3) ?

The integral of x^2cos(x/3) is 3x^2sin(x/3)-6(-3xcos(x/3)+9sin(x/3))+C

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integral of x^2cos(x/3)

\int x^{2} cos (\frac{x}{3}) d x

3 x^{2} sin (\frac{x}{3}) - 6 (- 3 x cos (\frac{x}{3}) + 9 sin (\frac{x}{3})) + C

Solution steps

\int x^{2} cos (\frac{x}{3}) d x

Apply Integration By Parts

: 3 x^{2} sin (\frac{x}{3}) - \int 6 x sin (\frac{x}{3}) d x

= 3 x^{2} sin (\frac{x}{3}) - \int 6 x sin (\frac{x}{3}) d x

\int 6 x sin (\frac{x}{3}) d x = 6 (- 3 x cos (\frac{x}{3}) + 9 sin (\frac{x}{3}))

= 3 x^{2} sin (\frac{x}{3}) - 6 (- 3 x cos (\frac{x}{3}) + 9 sin (\frac{x}{3}))

Add a constant to the solution

= 3 x^{2} sin (\frac{x}{3}) - 6 (- 3 x cos (\frac{x}{3}) + 9 sin (\frac{x}{3})) + C

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What is the integral of x^2cos(x/3) ?
The integral of x^2cos(x/3) is 3x^2sin(x/3)-6(-3xcos(x/3)+9sin(x/3))+C