What is the integral of x^2cos(1/6 x) ?

The integral of x^2cos(1/6 x) is 6x^2sin(1/6 x)-12(-6xcos(1/6 x)+36sin(1/6 x))+C

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integral of x^2cos(1/6 x)

\int x^{2} cos (\frac{1}{6} x) d x

6 x^{2} sin (\frac{1}{6} x) - 12 (- 6 x cos (\frac{1}{6} x) + 36 sin (\frac{1}{6} x)) + C

Solution steps

\int x^{2} cos (\frac{1}{6} x) d x

Apply Integration By Parts

: 6 x^{2} sin (\frac{1}{6} x) - \int 12 x sin (\frac{1}{6} x) d x

= 6 x^{2} sin (\frac{1}{6} x) - \int 12 x sin (\frac{1}{6} x) d x

\int 12 x sin (\frac{1}{6} x) d x = 12 (- 6 x cos (\frac{1}{6} x) + 36 sin (\frac{1}{6} x))

= 6 x^{2} sin (\frac{1}{6} x) - 12 (- 6 x cos (\frac{1}{6} x) + 36 sin (\frac{1}{6} x))

Add a constant to the solution

= 6 x^{2} sin (\frac{1}{6} x) - 12 (- 6 x cos (\frac{1}{6} x) + 36 sin (\frac{1}{6} x)) + C

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What is the integral of x^2cos(1/6 x) ?
The integral of x^2cos(1/6 x) is 6x^2sin(1/6 x)-12(-6xcos(1/6 x)+36sin(1/6 x))+C