What is the integral of (u-2)^3ln(u-2) ?

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

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integral of (u-2)^3ln(u-2)

\int (u - 2)^{3} ln (u - 2) d u

\frac{1}{4} ln (u - 2) (u - 2)^{4} - \frac{1}{16} (u - 2)^{4} + C

Solution steps

\int (u - 2)^{3} ln (u - 2) d u

Apply Integration By Parts

: \frac{1}{4} ln (u - 2) (u - 2)^{4} - \int \frac{1}{4} (u - 2)^{3} d u

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

\int \frac{1}{4} (u - 2)^{3} d u = \frac{1}{16} (u - 2)^{4}

= \frac{1}{4} ln (u - 2) (u - 2)^{4} - \frac{1}{16} (u - 2)^{4}

Add a constant to the solution

= \frac{1}{4} ln (u - 2) (u - 2)^{4} - \frac{1}{16} (u - 2)^{4} + C

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