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

The integral of x^2ln(x^4) is 4/3 x^3ln(x)-(4x^3)/9+C

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integral of x^2ln(x^4)

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

\frac{4}{3} x^{3} ln (x) - \frac{4 x ^{3}}{9} + C

Solution steps

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

Apply Integration By Parts

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

\int \frac{4 x ^{2}}{3} d x = \frac{4 x ^{3}}{9}

= \frac{1}{3} x^{3} ln (x^{4}) - \frac{4 x ^{3}}{9}

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

= \frac{4}{3} x^{3} ln (x) - \frac{4 x ^{3}}{9}

Add a constant to the solution

= \frac{4}{3} x^{3} ln (x) - \frac{4 x ^{3}}{9} + C

What is the integral of x^2ln(x^4) ?
The integral of x^2ln(x^4) is 4/3 x^3ln(x)-(4x^3)/9+C