What is the integral of x^4e^{(1-x^5)} ?

The integral of x^4e^{(1-x^5)} is -1/5 e^{1-x^5}+C

Popular >

integral of x^4e^{(1-x^5)}

\int x^{4} e^{(1 - x^{5})} d x

- \frac{1}{5} e^{1 - x^{5}} + C

Solution steps

\int x^{4} e^{1 - x^{5}} d x

Apply u-substitution

: \int - \frac{e ^{u}}{5} d u

= \int - \frac{e ^{u}}{5} d u

Take the constant out:

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

= - \frac{1}{5} \cdot \int e^{u} d u

Use the common integral:

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

= - \frac{1}{5} e^{u}

Substitute back

u = 1 - x^{5}

= - \frac{1}{5} e^{1 - x^{5}}

Add a constant to the solution

= - \frac{1}{5} e^{1 - x^{5}} + C

\frac{d y}{d x} + 5 y = 8

\frac{d}{d x} (sin (x^{2} + sin (x^{2} + sin (x^{2}))))

\int 16 x^{2} d x

\frac{d}{d x} (x ∣ x ∣^{∣ x ∣ - 1} (ln ∣ x ∣ + 1))

f (x) = x^{3}, at = 0

What is the integral of x^4e^{(1-x^5)} ?
The integral of x^4e^{(1-x^5)} is -1/5 e^{1-x^5}+C