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

The integral of x^2ln(x+4) is 1/3 x^3ln(x+4)-1/3 ((x^3)/3-2x^2+16x-64ln|x+4|)+C

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integral of x^2ln(x+4)

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

\frac{1}{3} x^{3} ln (x + 4) - \frac{1}{3} (\frac{x ^{3}}{3} - 2 x^{2} + 16 x - 64 ln ∣ x + 4 ∣) + 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{x ^{3}}{3 ( x + 4 )} d x

\int \frac{x ^{3}}{3 ( x + 4 )} d x = \frac{1}{3} (\frac{x ^{3}}{3} - 2 x^{2} + 16 x - 64 ln ∣ x + 4 ∣)

= \frac{1}{3} x^{3} ln (x + 4) - \frac{1}{3} (\frac{x ^{3}}{3} - 2 x^{2} + 16 x - 64 ln ∣ x + 4 ∣)

Add a constant to the solution

= \frac{1}{3} x^{3} ln (x + 4) - \frac{1}{3} (\frac{x ^{3}}{3} - 2 x^{2} + 16 x - 64 ln ∣ x + 4 ∣) + C

What is the integral of x^2ln(x+4) ?
The integral of x^2ln(x+4) is 1/3 x^3ln(x+4)-1/3 ((x^3)/3-2x^2+16x-64ln|x+4|)+C