What is the integral of x^22^{x^3} ?

The integral of x^22^{x^3} is (2^{x^3})/(3ln(2))+C

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integral of x^22^{x^3}

\int x^{2} 2^{x^{3}} d x

\frac{2 ^{x^{3}}}{3 ln ( 2 )} + C

Solution steps

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

Apply u-substitution

: \int \frac{2 ^{u^{\frac{3}{2}} - 1} u}{x} d u

= \int \frac{2 ^{u}}{3} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{3} \cdot \int 2^{u} d u

\int a^{x} d x = \frac{a ^{x}}{ln a}

= \frac{1}{3} \cdot \frac{2 ^{u}}{ln ( 2 )}

Substitute back

u = x^{3}

= \frac{1}{3} \cdot \frac{2 ^{x^{3}}}{ln ( 2 )}

Simplify

\frac{1}{3} \cdot \frac{2 ^{x^{3}}}{ln ( 2 )} : \frac{2 ^{x^{3}}}{3 ln ( 2 )}

= \frac{2 ^{x^{3}}}{3 ln ( 2 )}

Add a constant to the solution

= \frac{2 ^{x^{3}}}{3 ln ( 2 )} + C

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What is the integral of x^22^{x^3} ?
The integral of x^22^{x^3} is (2^{x^3})/(3ln(2))+C