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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply Integration By Parts

: \frac{1}{3} x^{3} ln (x^{3}) - \int x^{2} d x

= 4 (\frac{1}{3} x^{3} ln (x^{3}) - \int x^{2} d x)

\int x^{2} d x = \frac{x ^{3}}{3}

= 4 (\frac{1}{3} x^{3} ln (x^{3}) - \frac{x ^{3}}{3})

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

= 4 (x^{3} ln (x) - \frac{x ^{3}}{3})

Add a constant to the solution

= 4 (x^{3} ln (x) - \frac{x ^{3}}{3}) + C

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What is the integral of 4x^2ln(x^3) ?
The integral of 4x^2ln(x^3) is 4(x^3ln(x)-(x^3)/3)+C