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

\int cos (2 t) d t

\int (x^{3} - \frac{1}{x ^{2}})^{2} d x

\int x^{2} - 7 x + 12 d x

\int y^{- \frac{3}{2}} d y

\int - 2 t + 3 d t

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