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

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

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integral of cos(x)x^3

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

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

Solution steps

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

Apply Integration By Parts

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

= 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

\int (lo g_{2} (x))^{2} d x

\int e^{x} 36 + e^{x} d x

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\int (\frac{1}{x ^{\frac{3}{2}}}) d x

\int 0 sin (x) d x

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