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

The integral of-e^{2x^3}x^2 is -1/6 e^{2x^3}+C

Popular >

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

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

- \frac{1}{6} e^{2 x^{3}} + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

: \int \frac{e ^{u}}{6} d u

= - \int \frac{e ^{u}}{6} d u

Take the constant out:

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

= - \frac{1}{6} \cdot \int e^{u} d u

Use the common integral:

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

= - \frac{1}{6} e^{u}

Substitute back

u = 2 x^{3}

= - \frac{1}{6} e^{2 x^{3}}

Add a constant to the solution

= - \frac{1}{6} e^{2 x^{3}} + C

\int x e^{3 - 4 x^{2}} d x

\int \frac{( ln ( x ) )}{x} d x

\int \frac{24 x}{2 x + 3} d x

\int \frac{3}{25 + 16 x ^{2}} d x

\int 9 sec (x) tan (x) d x

What is the integral of-e^{2x^3}x^2 ?
The integral of-e^{2x^3}x^2 is -1/6 e^{2x^3}+C