What is the integral of z3^{z^2} ?

The integral of z3^{z^2} is 1/(2ln(3))*3^{z^2}+C

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integral of z3^{z^2}

\int z 3^{z^{2}}

\frac{1}{2 ln ( 3 )} \cdot 3^{z^{2}} + C

Solution steps

\int z \cdot 3^{z^{2}} d z

Apply u-substitution

: \int \frac{1}{2 ln ( 3 )} d u

= \int \frac{1}{2 ln ( 3 )} d u

Integral of a constant:

\int a d x = a x

= \frac{1}{2 ln ( 3 )} u

Substitute back

u = 3^{z^{2}}

= \frac{1}{2 ln ( 3 )} \cdot 3^{z^{2}}

Add a constant to the solution

= \frac{1}{2 ln ( 3 )} \cdot 3^{z^{2}} + C

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What is the integral of z3^{z^2} ?
The integral of z3^{z^2} is 1/(2ln(3))*3^{z^2}+C