What is the integral of z^3cos(x)+2xy^2 ?

The integral of z^3cos(x)+2xy^2 is z^3sin(x)+y^2x^2+C

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integral of z^3cos(x)+2xy^2

\int z^{3} cos (x) + 2 x y^{2} d x

z^{3} sin (x) + y^{2} x^{2} + C

Solution steps

\int z^{3} cos (x) + 2 x y^{2} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int cos (x) z^{3} d x + \int 2 y^{2} x d x

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

\int 2 y^{2} x d x = y^{2} x^{2}

= z^{3} sin (x) + y^{2} x^{2}

Add a constant to the solution

= z^{3} sin (x) + y^{2} x^{2} + C

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What is the integral of z^3cos(x)+2xy^2 ?
The integral of z^3cos(x)+2xy^2 is z^3sin(x)+y^2x^2+C