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

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

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integral of x^3*cos(x)

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

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

Solution steps

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

Apply Integration By Parts

= 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)))

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

Add a constant to the solution

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

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