What is the integral from 0 to 1 of x29^{x^2} ?

The integral from 0 to 1 of x29^{x^2} is (14)/(ln(29))

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integral from 0 to 1 of x29^{x^2}

\int_{0}^{1} x 2 9^{x^{2}} d x

\frac{14}{ln ( 29 )}

Decimal

4.15763 \dots

Solution steps

\int_{0}^{1} x \cdot 2 9^{x^{2}} d x

Apply u-substitution

: \int_{1}^{29} \frac{1}{2 ln ( 29 )} d u

= \int_{1}^{29} \frac{1}{2 ln ( 29 )} d u

Integral of a constant:

\int a d x = a x

= [\frac{1}{2 ln ( 29 )} u]_{1}^{29}

Compute the boundaries:

\frac{14}{ln ( 29 )}

= \frac{14}{ln ( 29 )}

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What is the integral from 0 to 1 of x29^{x^2} ?
The integral from 0 to 1 of x29^{x^2} is (14)/(ln(29))