What is the integral of x3^{x^2} ?

The integral of x3^{x^2} is 1/(2ln(3))*3^{x^2}+C

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integral of x3^{x^2}

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

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

Solution steps

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

f (x) = 2 - \frac{4}{x}

\int 4 sin^{2} (2 x) d x

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

\frac{d y}{d x} = e^{y} cos (2 x)

f (t) = 2 cos (t)

What is the integral of x3^{x^2} ?
The integral of x3^{x^2} is 1/(2ln(3))*3^{x^2}+C