What is the integral of x^3sqrt(x^2) ?

The integral of x^3sqrt(x^2) is (x^5)/5+C

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integral of x^3sqrt(x^2)

\int x^{3} x^{2} d x

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

Solution steps

\int x^{3} x^{2} d x

x^{2} = (x),

assuming

x \geq 0

= \int x^{3} x d x

Simplify

x^{3} x : x^{4}

= \int x^{4} d x

Apply the Power Rule

: \frac{x ^{5}}{5}

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

Add a constant to the solution

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

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What is the integral of x^3sqrt(x^2) ?
The integral of x^3sqrt(x^2) is (x^5)/5+C