What is the integral of x^3In^2x ?

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

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integral of x^3In^2x

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

\frac{I n ^{2} x ^{5}}{5} + C

Solution steps

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

Take the constant out:

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

= I n^{2} \cdot \int x x^{3} d x

Simplify

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

= I n^{2} \cdot \int x^{4} d x

Apply the Power Rule

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

= I n^{2} \frac{x ^{5}}{5}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{I n ^{2} x ^{5}}{5}

Add a constant to the solution

= \frac{I n ^{2} x ^{5}}{5} + C

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