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

The integral of x^4e(1-x^5) is e((x^5)/5-(x^{10})/(10))+C

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

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

e (\frac{x ^{5}}{5} - \frac{x ^{10}}{10}) + C

Solution steps

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

Take the constant out:

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

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

Expand

x^{4} (1 - x^{5}) : x^{4} - x^{9}

= e \cdot \int x^{4} - x^{9} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= e (\int x^{4} d x - \int x^{9} d x)

\int x^{4} d x = \frac{x ^{5}}{5}

\int x^{9} d x = \frac{x ^{10}}{10}

= e (\frac{x ^{5}}{5} - \frac{x ^{10}}{10})

Add a constant to the solution

= e (\frac{x ^{5}}{5} - \frac{x ^{10}}{10}) + C

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What is the integral of x^4e(1-x^5) ?
The integral of x^4e(1-x^5) is e((x^5)/5-(x^{10})/(10))+C