What is the integral of 11x^2e^{-4x^3} ?

The integral of 11x^2e^{-4x^3} is -11/12 e^{-4x^3}+C

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integral of 11x^2e^{-4x^3}

\int 11 x^{2} e^{- 4 x^{3}} d x

- \frac{11}{12} e^{- 4 x^{3}} + C

Solution steps

\int 11 x^{2} e^{- 4 x^{3}} d x

Take the constant out:

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

= 11 \cdot \int x^{2} e^{- 4 x^{3}} d x

Apply u-substitution

: \int - \frac{e ^{u}}{12} d u

= 11 \cdot \int - \frac{e ^{u}}{12} d u

Take the constant out:

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

= 11 (- \frac{1}{12} \cdot \int e^{u} d u)

Use the common integral:

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

= 11 (- \frac{1}{12} e^{u})

Substitute back

u = - 4 x^{3}

= 11 (- \frac{1}{12} e^{- 4 x^{3}})

Simplify

11 (- \frac{1}{12} e^{- 4 x^{3}}) : - \frac{11}{12} e^{- 4 x^{3}}

= - \frac{11}{12} e^{- 4 x^{3}}

Add a constant to the solution

= - \frac{11}{12} e^{- 4 x^{3}} + C

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What is the integral of 11x^2e^{-4x^3} ?
The integral of 11x^2e^{-4x^3} is -11/12 e^{-4x^3}+C