What is the integral from 1 to sqrt(2 of)x5^{x^2} ?

The integral from 1 to sqrt(2 of)x5^{x^2} is (10)/(ln(5))

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integral from 1 to sqrt(2 of)x5^{x^2}

\int_{1}^{2} x 5^{x^{2}} d x

\frac{10}{ln ( 5 )}

Decimal

6.21334 \dots

Solution steps

\int_{1}^{2} x \cdot 5^{x^{2}} d x

Apply u-substitution

: \int_{5}^{25} \frac{1}{2 ln ( 5 )} d u

= \int_{5}^{25} \frac{1}{2 ln ( 5 )} d u

Integral of a constant:

\int a d x = a x

= [\frac{1}{2 ln ( 5 )} u]_{5}^{25}

Compute the boundaries:

\frac{10}{ln ( 5 )}

= \frac{10}{ln ( 5 )}

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What is the integral from 1 to sqrt(2 of)x5^{x^2} ?
The integral from 1 to sqrt(2 of)x5^{x^2} is (10)/(ln(5))