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

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

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integral of x^3ln(x^4)

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

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

Add a constant to the solution

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

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