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

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

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

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

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

Solution steps

\int 2 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

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

Apply u-substitution

= 2 \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

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

Use the common integral:

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

= 2 \cdot \frac{1}{3} e^{u}

Substitute back

u = x^{3}

= 2 \cdot \frac{1}{3} e^{x^{3}}

Simplify

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

= \frac{2}{3} e^{x^{3}}

Add a constant to the solution

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

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

t a y l or e^{x} + 0 + 5

x \to 0 lim ((1 + 4 x)^{\frac{3}{x}})

\int (\frac{tan ( u )}{4} - \frac{4}{7} u^{6} - \frac{2}{u}) d u

x \to a lim (\frac{1}{2})

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