What is the integral of y^2z+2xz^2 ?

The integral of y^2z+2xz^2 is y^2zx+z^2x^2+C

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integral of y^2z+2xz^2

\int y^{2} z + 2 x z^{2} d x

y^{2} z x + z^{2} x^{2} + C

Solution steps

\int y^{2} z + 2 x z^{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 y^{2} z d x + \int 2 z^{2} x d x

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

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

= y^{2} z x + z^{2} x^{2}

Add a constant to the solution

= y^{2} z x + z^{2} x^{2} + C

What is the integral of y^2z+2xz^2 ?
The integral of y^2z+2xz^2 is y^2zx+z^2x^2+C