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}}{3} 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 (- \frac{1}{3} \cdot \int e^{u} d u)

Use the common integral:

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

= 6 (- \frac{1}{3} e^{u})

Substitute back

u = - x^{3}

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

Simplify

6 (- \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{2 t}{1 + t} d t

\int cos (2 x) ln (tan (x)) d x

\int \frac{x ^{3} + 1}{x ^{3} + 4 x ^{2} + 5 x} d x

\int (\frac{t ^{4}}{2} - \frac{3}{t ^{- 2}} + 3 t) d t

\int \frac{+ y}{y} d y

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