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

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

Popular >

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

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

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

Solution steps

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

Apply u-substitution

: \int \frac{e ^{u}}{3} 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{d}{d x} (arctan (sinh (x)))

\frac{d}{d x} ((a x^{2} + b x + c) e^{- \frac{x}{4}})

f (x) = \frac{14}{( 1 + e ^{- x} ) , at ( 0 , 7 )}

\int \frac{1}{( sin ( x ) ) ^{4}} d x

\frac{\partial}{\partial y} (2 x^{3} y + 1)

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