What is the integral of xye^{xz}+z^3 ?

The integral of xye^{xz}+z^3 is (z^4)/4+ye^{xz}+C

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integral of xye^{xz}+z^3

\int x y e^{x z} + z^{3} d z

\frac{z ^{4}}{4} + y e^{x z} + C

Solution steps

\int x y e^{x z} + z^{3} d z

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

\int z^{3} d z = \frac{z ^{4}}{4}

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

= \frac{z ^{4}}{4} + y e^{x z}

Add a constant to the solution

= \frac{z ^{4}}{4} + y e^{x z} + C

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What is the integral of xye^{xz}+z^3 ?
The integral of xye^{xz}+z^3 is (z^4)/4+ye^{xz}+C