The Student Room Group

Hard integration by substitution exam question

0CCD0309-83E0-475F-8CA1-E582E4A73ADC.jpeg
Can someone please walkthrough this question with me, thanks.
Reply 1
Maybe a hint.

4x3=2[(x2+3)3](2x)4x^3 = 2[(x^2+3)-3](2x).

Comment: Perhaps a bit of working will help see why I do this. Remember our goal is to make all the x's to u's, and all the dx's into du's.
(edited 11 months ago)
Reply 2
Original post by tonyiptony
Maybe a hint.

4x3=2[(x2+3)3](2x)4x^3 = 2[(x^2+3)-3](2x).

Comment: Perhaps a bit of working will help see why I do this. Remember our goal is to make all the x's to u's, and all the dx's into du's.

I am still so stuck, sorry.
Reply 3
Original post by Matheen1
I am still so stuck, sorry.


Freebies first. Do the standard substitution step, so...
"Let u^2=x^2+3, (2u)du=(2x)dx".

We want to replace all the "x^2+3"s with "u^2", and the "(2x)dx" with "(2u)du". That's what we normally do in substitution, right?
But we don't have x^2+3 in the numerator... So make one with some finagling (see #2).

Then we should have something that's (much) easier to integrate.
(edited 11 months ago)

Quick Reply

Latest