What is the integral of 3^{x^2}x ?

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

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integral of 3^{x^2}x

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

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

Solution steps

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

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^{x^{2}}

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

Add a constant to the solution

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

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