What is the integral of x^2cos(1/9 x) ?

The integral of x^2cos(1/9 x) is 9x^2sin(1/9 x)-18(-9xcos(1/9 x)+81sin(1/9 x))+C

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integral of x^2cos(1/9 x)

\int x^{2} cos (\frac{1}{9} x) d x

9 x^{2} sin (\frac{1}{9} x) - 18 (- 9 x cos (\frac{1}{9} x) + 81 sin (\frac{1}{9} x)) + C

Solution steps

\int x^{2} cos (\frac{1}{9} x) d x

Apply Integration By Parts

= 9 x^{2} sin (\frac{1}{9} x) - \int 18 x sin (\frac{1}{9} x) d x

\int 18 x sin (\frac{1}{9} x) d x = 18 (- 9 x cos (\frac{1}{9} x) + 81 sin (\frac{1}{9} x))

= 9 x^{2} sin (\frac{1}{9} x) - 18 (- 9 x cos (\frac{1}{9} x) + 81 sin (\frac{1}{9} x))

Add a constant to the solution

= 9 x^{2} sin (\frac{1}{9} x) - 18 (- 9 x cos (\frac{1}{9} x) + 81 sin (\frac{1}{9} x)) + C

What is the integral of x^2cos(1/9 x) ?
The integral of x^2cos(1/9 x) is 9x^2sin(1/9 x)-18(-9xcos(1/9 x)+81sin(1/9 x))+C