What is the integral of 6x^2e^{x^3} ?

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

Popular >

integral of 6x^2e^{x^3}

\int 6 x^{2} e^{x^{3}} d x

2 e^{x^{3}} + C

Solution steps

\int 6 x^{2} e^{x^{3}} d x

Take the constant out:

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

= 6 \cdot \int x^{2} e^{x^{3}} d x

Apply u-substitution

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

= 6 \cdot \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

= 6 \cdot \frac{1}{3} \cdot \int e^{u} d u

Use the common integral:

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

= 6 \cdot \frac{1}{3} e^{u}

Substitute back

u = x^{3}

= 6 \cdot \frac{1}{3} e^{x^{3}}

Simplify

6 \cdot \frac{1}{3} e^{x^{3}} : 2 e^{x^{3}}

= 2 e^{x^{3}}

Add a constant to the solution

= 2 e^{x^{3}} + C

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

\frac{\partial}{\partial x} (x y e^{yz})

\int_{- 1}^{5} ∣ 2 x - 3 ∣ d x

\frac{d}{d t} (\frac{1 - 2 t}{1 + 2 t})

- \frac{2 s + 1}{s ^{2} + 3 s + 2}