Question

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

Answer 1

`\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`