What is the integral of x^2ln(100) ?

The integral of x^2ln(100) is 2/3 ln(10)x^3+C

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integral of x^2ln(100)

\int x^{2} ln (100) d x

\frac{2}{3} ln (10) x^{3} + C

Solution steps

\int x^{2} ln (100) d x

Take the constant out:

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

= ln (100) \cdot \int x^{2} d x

ln (100) = 2 ln (10)

= 2 ln (10) \cdot \int x^{2} d x

Apply the Power Rule

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

Simplify

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

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

Add a constant to the solution

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

What is the integral of x^2ln(100) ?
The integral of x^2ln(100) is 2/3 ln(10)x^3+C