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

The integral of x^3cos(y) is x^3sin(y)+C

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integral of x^3cos(y)

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

x^{3} sin (y) + C

Solution steps

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

Take the constant out:

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

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

Use the common integral:

\int cos (y) d y = sin (y)

= x^{3} sin (y)

Add a constant to the solution

= x^{3} sin (y) + C