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

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

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integral of x^2cos(x/9)

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

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\frac{\partial}{\partial x} (4 y e^{5 x^{2} - 6 y})

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