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

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

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

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

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

Solution steps

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

\int z^{3} d x = z^{3} x

\int 2 cos (x) y^{2} d x = 2 y^{2} sin (x)

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

Add a constant to the solution

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

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