What is the integral of x^4In^5x ?

The integral of x^4In^5x is (In^5x^6)/6+C

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integral of x^4In^5x

\int x^{4} I n^{5} x d x

\frac{I n ^{5} x ^{6}}{6} + C

Solution steps

\int x^{4} I n^{5} x d x

Take the constant out:

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

= I n^{5} \cdot \int x x^{4} d x

Simplify

x x^{4} : x^{5}

= I n^{5} \cdot \int x^{5} d x

Apply the Power Rule

: \frac{x ^{6}}{6}

= I n^{5} \frac{x ^{6}}{6}

Multiply fractions:

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

= \frac{I n ^{5} x ^{6}}{6}

Add a constant to the solution

= \frac{I n ^{5} x ^{6}}{6} + C

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