What is the integral of ze^{4z^2} ?

The integral of ze^{4z^2} is 1/8 e^{4z^2}+C

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integral of ze^{4z^2}

\int z e^{4 z^{2}} d z

\frac{1}{8} e^{4 z^{2}} + C

Solution steps

\int z e^{4 z^{2}} d z

Apply u-substitution

: \int \frac{e ^{u}}{8} d u

= \int \frac{e ^{u}}{8} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{8} \cdot \int e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= \frac{1}{8} e^{u}

Substitute back

u = 4 z^{2}

= \frac{1}{8} e^{4 z^{2}}

Add a constant to the solution

= \frac{1}{8} e^{4 z^{2}} + C

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