What is the integral of (x^2)*e^{x^3} ?

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

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integral of (x^2)*e^{x^3}

integral

(x^{2}) \cdot e^{x^{3}}

\frac{1}{3} e^{x^{3}} + C

Solution steps

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

Apply u-substitution

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

= \int \frac{e ^{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 e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= \frac{1}{3} e^{u}

Substitute back

u = x^{3}

= \frac{1}{3} e^{x^{3}}

Add a constant to the solution

= \frac{1}{3} e^{x^{3}} + C

\frac{2}{( ( x - 2 ) x + 2 )}

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

\frac{2 x}{( x + 1 ) ^{2} ( x ^{2} + 2 )}

\frac{sin ( x )}{( 1 + ( cos ( x ) ) ^{2} )}

\frac{7 x ^{3} - 5 x ^{2} + 7 x - 8}{x ^{2}}

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