How do you evaluate \int 5( 4- 3x ) ^ { 6} d x?

1 Answer
Feb 6, 2018

\mbox{The answer is:} \qquad-5/21 (4-3x)^7 + C

Explanation:

\

\mbox{This can be achieved by a simple substitution} \ \ \mbox{ [ or even by sight, if you can see it ].}

\mbox{Substitution:} \qquad u=4-3x

\mbox{Thus:} \qquad du=-3dx

\mbox{Solving for} \ dx: \qquad dx=-{du}/3

\mbox{Hence, the integral:} \qquad \int 5(4-3x)^6dx=\int 5u^6(-{du}/3)=-5/3\intu^6du=-5/3 u^7/7=-5/21(4-3x)^7+C