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

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

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integral of-cos(x)3x^2

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

- 3 (x^{2} sin (x) - 2 (- x cos (x) + sin (x))) + C

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - 3 \cdot \int cos (x) x^{2} d x

Apply Integration By Parts

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

\int 2 x sin (x) d x = 2 (- x cos (x) + sin (x))

= - 3 (x^{2} sin (x) - 2 (- x cos (x) + sin (x)))

Add a constant to the solution

= - 3 (x^{2} sin (x) - 2 (- x cos (x) + sin (x))) + C

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