What is the integral from 0 to 3 of x5^{x^2} ?

The integral from 0 to 3 of x5^{x^2} is (976562)/(ln(5))

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integral from 0 to 3 of x5^{x^2}

\int_{0}^{3} x 5^{x^{2}} d x

\frac{976562}{ln ( 5 )}

Decimal Notation

606772.08636 \dots

Solution steps

\int_{0}^{3} x \cdot 5^{x^{2}} d x

Apply u-substitution

: \int_{1}^{1953125} \frac{1}{2 ln ( 5 )} d u

= \int_{1}^{1953125} \frac{1}{2 ln ( 5 )} d u

Integral of a constant:

\int a d x = a x

= [\frac{1}{2 ln ( 5 )} u]_{1}^{1953125}

Compute the boundaries:

\frac{976562}{ln ( 5 )}

= \frac{976562}{ln ( 5 )}

\int_{0}^{1} \frac{5 r}{( 4 + r ^{2} ) ^{2}} d r

\int_{1}^{1} 1

\int_{- 5}^{1} (x^{2} + 4 x - 5) d x

\int_{0}^{1} x^{2} (x + \frac{1}{2}) d x

\int_{0}^{1} 10 e^{x + 3} d x

What is the integral from 0 to 3 of x5^{x^2} ?
The integral from 0 to 3 of x5^{x^2} is (976562)/(ln(5))