What is the integral from 1 to sqrt(3 of)x3^{x^2} ?

The integral from 1 to sqrt(3 of)x3^{x^2} is (12)/(ln(3))

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integral from 1 to sqrt(3 of)x3^{x^2}

\int_{1}^{3} x 3^{x^{2}} d x

\frac{12}{ln ( 3 )}

Decimal

10.92287 \dots

Solution steps

\int_{1}^{3} x \cdot 3^{x^{2}} d x

Apply u-substitution

= \int_{3}^{27} \frac{1}{2 ln ( 3 )} d u

Integral of a constant:

\int a d x = a x

= [\frac{1}{2 ln ( 3 )} u]_{3}^{27}

Compute the boundaries:

\frac{12}{ln ( 3 )}

= \frac{12}{ln ( 3 )}

What is the integral from 1 to sqrt(3 of)x3^{x^2} ?
The integral from 1 to sqrt(3 of)x3^{x^2} is (12)/(ln(3))