What is the integral of x^2*10^{x^3} ?

The integral of x^2*10^{x^3} is 1/(3ln(10))*10^{x^3}+C

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integral of x^2*10^{x^3}

\int x^{2} \cdot 1 0^{x^{3}} d x

\frac{1}{3 ln ( 10 )} \cdot 1 0^{x^{3}} + C

Solution steps

\int x^{2} \cdot 1 0^{x^{3}} d x

Apply u-substitution

: \int \frac{1}{3 ln ( 10 )} d u

= \int \frac{1}{3 ln ( 10 )} d u

Integral of a constant:

\int a d x = a x

= \frac{1}{3 ln ( 10 )} u

Substitute back

u = 1 0^{x^{3}}

= \frac{1}{3 ln ( 10 )} \cdot 1 0^{x^{3}}

Add a constant to the solution

= \frac{1}{3 ln ( 10 )} \cdot 1 0^{x^{3}} + C

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What is the integral of x^2*10^{x^3} ?
The integral of x^2*10^{x^3} is 1/(3ln(10))*10^{x^3}+C