Solving an Integral Problem: Finding the Minus Sign

[Jalo]

Homework Statement

(ignore what's written, it isn't important for the problem)

I'm studying integrals and I came across this solved example. However I can't understand where the minus of the integral came from came from.

Homework Equations

The Attempt at a Solution

The primitive of a f^p * f ' function is f^(p+1) / (p+1) Therefore it should be ln^2(x-1)/2 and not -ln^2(x-1)/2

Thanks

 

[Screwdriver]

You could dispel any doubts by making a u-substitution. Try $u = 1 - x$ and see where that takes you.

 

[SammyS]

Homework Statement

(ignore what's written, it isn't important for the problem)

I'm studying integrals and I came across this solved example. However I can't understand where the minus of the integral came from came from.

Homework Equations

The Attempt at a Solution

The primitive of a f^p * f ' function is f^(p+1) / (p+1) Therefore it should be ln^2(x-1)/2 and not -ln^2(x-1)/2

Thanks

By the chain rule: $\displaystyle \frac{d}{dx}\ln(1-x)=\frac{1}{1-x}\frac{d}{dx}(1-x)=-\frac{1}{1-x}\,.$

So you have the anti-derivative of f^p * (- f ' ) .