Because precisely equals for . We want to represent the integrand in this form because, as the text says,
I am being asked to find the indefinite integral
The solution reads as:
The factor in the integrand is, except for a constant multiple, the derivative of ,
so that we can apply equation
with and .
Since , we write before applying the formula.
Thus we have
Why the and why the outside of the integral?
Many thanks all.
So if I see a question like this, I should find the derivative of what's inside the brackets, if it matches what's outside the brackets (but has a numerical multiple) then I use the equation above, but include a fraction to counter the numerical multiple so it equals 1? And the numerical fraction (in this case a half to cancel the 2 to a 1) goes outside the integral to comply with the constant multiple rule?
(struggling a little here)