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The integral can be found in more than one way. First use integration by parts, then expand the expression and integrate the result.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(2x6)(x-1{)}^{2}dx$

Identify $u$ and dv when integrating this expression using integration by parts.

$u=dv=dx$

Expand the terms within the integrand.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}dx$

$($Simplify your answer.$)$

Evaluate the integral.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(2x6)(x-1{)}^{2}dx=\frac{(2x6)(x-1{)}^3}{3}-\frac{(x-1{)}^4}{6}c$