What is the integral of x*5^{x^2} ?

The integral of x*5^{x^2} is 1/(2ln(5))*5^{x^2}+C

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integral of x*5^{x^2}

\int x \cdot 5^{x^{2}} d x

\frac{1}{2 ln ( 5 )} \cdot 5^{x^{2}} + C

Solution steps

\int x \cdot 5^{x^{2}} d x

Apply u-substitution

: \int \frac{1}{2 ln ( 5 )} d u

= \int \frac{1}{2 ln ( 5 )} d u

Integral of a constant:

\int a d x = a x

= \frac{1}{2 ln ( 5 )} u

Substitute back

u = 5^{x^{2}}

= \frac{1}{2 ln ( 5 )} \cdot 5^{x^{2}}

Add a constant to the solution

= \frac{1}{2 ln ( 5 )} \cdot 5^{x^{2}} + C

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What is the integral of x*5^{x^2} ?
The integral of x*5^{x^2} is 1/(2ln(5))*5^{x^2}+C