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

The integral of ln(4)x^2 is 2/3 ln(2)x^3+C

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integral of ln(4)x^2

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

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

Solution steps

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

Take the constant out:

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

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

ln (4) = 2 ln (2)

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

Apply the Power Rule

: \frac{x ^{3}}{3}

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

Simplify

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

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

Add a constant to the solution

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

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