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

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

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

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

(\frac{4}{5} x)^{3}

1 - 2 x^{2}

y^{^{'}} = \frac{( x ^{2} + 1 )}{3 y ^{2}}

e^{x^{3}}

y^{^{''}} + y^{^{'}} = a \cdot x^{2} + b \cdot x^{3}

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