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Popular >

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

Solution

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

Solution

- \frac{1}{4} e^{- x^{4}} + C

Solution steps

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

Apply u-substitution

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

= \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

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

Use the common integral:

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

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

Substitute back

u = - x^{4}

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

Add a constant to the solution

= - \frac{1}{4} e^{- x^{4}} + C

Popular Examples

integral of cot^2(1)

\int cot^{2} (1) d x

y^{''}-6y^'+8y=e^{3t}

y^{^{''}} - 6 y^{^{'}} + 8 y = e^{3 t}

integral of (x^4+x-1)/(x^2+1)

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

integral of (x^3-2x+3)/(x^2-x+1)

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

(\partial)/(\partial x)((1-x)+10(y-x^2)^2)

\frac{\partial}{\partial x} ((1 - x) + 10 (y - x^{2})^{2})

Frequently Asked Questions (FAQ)

What is the integral of x^3*e^{-x^4} ?
The integral of x^3*e^{-x^4} is -1/4 e^{-x^4}+C