u-substitution: can someone explain to me how my book has this answer?

Question

anonymous · Answer

attachment

anonymous · Answer

the answer i got was...$$\frac{ \left( 4-2x \right)^{4} }{ 4 }$$

isaiah.feynman · Answer

Let u = 4-2x right?

anonymous · Answer

yes! thats what i put as my u

isaiah.feynman · Answer

Working on it.

isaiah.feynman · Answer

Strange even the book is wrong.

anonymous · Answer

how weird! did you get the same answer as me?

isaiah.feynman · Answer

Nope. The calculations are lengthy lol. I will post in a bit.

isaiah.feynman · Answer

I found the correct answer. The book is wrong.

anonymous · Answer

so weird! ill have to ask my professor about this one -_- I totally appreciate the help!!

isaiah.feynman · Answer

So the solution to that integration is $$-\frac{ 1 }{2}\left( \frac{(4-2x) ^{4} }{ 4 } \right) + C $$

isaiah.feynman · Answer

If you solve an integral, take the derivative of your answer, if the derivative is the same as the integral you were solving then your integration is right.