What is the integral of-4x^3e^{-x^4} ?

The integral of-4x^3e^{-x^4} is e^{-x^4}+C

Popular >

integral of-4x^3e^{-x^4}

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

e^{- x^{4}} + C

Solution steps

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

Take the constant out:

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

= - 4 \cdot \int x^{3} e^{- x^{4}} d x

Apply u-substitution

: \int - \frac{e ^{u}}{4} d u

= - 4 \cdot \int - \frac{e ^{u}}{4} d u

Take the constant out:

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

= - 4 (- \frac{1}{4} \cdot \int e^{u} d u)

Use the common integral:

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

= - 4 (- \frac{1}{4} e^{u})

Substitute back

u = - x^{4}

= - 4 (- \frac{1}{4} e^{- x^{4}})

Simplify

- 4 (- \frac{1}{4} e^{- x^{4}}) : e^{- x^{4}}

= e^{- x^{4}}

Add a constant to the solution

= e^{- x^{4}} + C

\int e^{- 3 x} sin (\frac{x}{3}) d x

\int \frac{cot ( x )}{4 - csc ^{2} ( x )} d x

\int \frac{sec ( y )}{sec ( y ) - 1} d y

\int sec^{2} (x) ln (cos (x)) d x

\int \frac{cos ( x )}{2 x} d x

What is the integral of-4x^3e^{-x^4} ?
The integral of-4x^3e^{-x^4} is e^{-x^4}+C