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

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

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integral of 3x^3cos(x)

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

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

Solution steps

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

Take the constant out:

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

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

Apply Integration By Parts

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

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

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

Add a constant to the solution

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

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