What is the integral of x^2+xy^2+z ?

The integral of x^2+xy^2+z is zx+(x^3)/3+(y^2x^2)/2+C

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integral of x^2+xy^2+z

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

z x + \frac{x ^{3}}{3} + \frac{y ^{2} x ^{2}}{2} + C

Solution steps

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

\int z d x = z x

\int x^{2} d x = \frac{x ^{3}}{3}

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

= z x + \frac{x ^{3}}{3} + \frac{y ^{2} x ^{2}}{2}

Add a constant to the solution

= z x + \frac{x ^{3}}{3} + \frac{y ^{2} x ^{2}}{2} + C

\frac{4}{x - 5}

\frac{\partial}{\partial x} (\frac{x}{y + 2 z})

\int e^{- \frac{y}{2}} d y

sin (x) + 5 π x

\frac{1}{8} (e^{4 x} + e^{- 4 x})

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