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

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 )}

x \to 0 lim (\frac{3 x ^{2} - 2 x}{x})

\int \frac{e ^{2 x} - 6 e ^{x}}{e ^{2 x} + 11} d x

t an g e n t f (x) = 20 x + 5

\int \frac{e ^{\frac{1}{x ^{4}}}}{x ^{5}} d x

x \to 2 lim (\frac{4 x - 3}{x + 2})

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))