What is the integral of ln(3)x^4*2x^5 ?

The integral of ln(3)x^4*2x^5 is 1/5 ln(3)x^{10}+C

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integral of ln(3)x^4*2x^5

\int ln (3) x^{4} \cdot 2 x^{5} d x

\frac{1}{5} ln (3) x^{10} + C

Solution steps

\int ln (3) x^{4} \cdot 2 x^{5} d x

Take the constant out:

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

= ln (3) \cdot 2 \cdot \int x^{4} x^{5} d x

Simplify

x^{4} x^{5} : x^{9}

= ln (3) \cdot 2 \cdot \int x^{9} d x

Apply the Power Rule

= ln (3) \cdot 2 \cdot \frac{x ^{10}}{10}

Simplify

ln (3) \cdot 2 \cdot \frac{x ^{10}}{10} : \frac{1}{5} ln (3) x^{10}

= \frac{1}{5} ln (3) x^{10}

Add a constant to the solution

= \frac{1}{5} ln (3) x^{10} + C

What is the integral of ln(3)x^4*2x^5 ?
The integral of ln(3)x^4*2x^5 is 1/5 ln(3)x^{10}+C