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

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

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

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

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

Solution steps

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

Apply u-substitution

: \int \frac{e ^{u^{\frac{5}{4}}} u ^{\frac{1}{4}}}{4} d u

= \int \frac{e ^{u^{\frac{5}{4}}} u ^{\frac{1}{4}}}{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^{\frac{5}{4}}} u^{\frac{1}{4}} d u

Apply u-substitution

: \int \frac{4 e ^{v}}{5} d v

= \frac{1}{4} \cdot \int \frac{4 e ^{v}}{5} d v

Take the constant out:

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

= \frac{1}{4} \cdot \frac{4}{5} \cdot \int e^{v} d v

Use the common integral:

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

= \frac{1}{4} \cdot \frac{4}{5} e^{v}

Substitute back

= \frac{1}{4} \cdot \frac{4}{5} e^{(x^{4})^{\frac{5}{4}}}

Simplify

\frac{1}{4} \cdot \frac{4}{5} e^{(x^{4})^{\frac{5}{4}}} : \frac{1}{5} e^{x^{5}}

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

Add a constant to the solution

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

x \to 5 lim (\frac{x ^{2} + 1}{x - 5})

\frac{1}{s ^{2} - 2 s + 3}

\frac{\partial}{\partial x} (3 x^{2} - 2 x + 6 y^{2} + 2 y + 2)

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

\frac{\partial}{\partial x} (4 y - 2 x y)

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