The Student Room Group
Uni students - Complete our survey >>
Uni students - Complete our survey >>
Uni students - Complete our survey >>

C3 Integration question HELP!!!

find the integral of 1+x/sqrt(x+x^2)

how would you go about answering that question ?
Reply 1
Avatar for Notnek
Notnek
21
Original post by HUBWD
find the integral of 1+x/sqrt(x+x^2)

how would you go about answering that question ?

Is 1+x the numerator? Please add brackets to make your question clearer.
Reply 2
Avatar for HUBWD
HUBWD
OP
6
Original post by notnek
Is 1+x the numerator? Please add brackets to make your question clearer.


yea, it will be (1+x)/sqrt(x+x^2)
Reply 3
Avatar for Notnek
Notnek
21
Original post by HUBWD
yea, it will be (1+x)/sqrt(x+x^2)

Start by completing the square inside the square root then substitute what you get inside the brackets that you've generated.
I don't think its possible, 1/(x+x^2)^1/2 requires hyperbolic substitution or something to be able to integrate it.
Reply 5
Avatar for andrewmc96
andrewmc96
2
Original post by tsumannai
I don't think its possible, 1/(x+x^2)^1/2 requires hyperbolic substitution or something to be able to integrate it.


I'm fairly sure that it's possible using a trig substitution
Original post by andrewmc96
I'm fairly sure that it's possible using a trig substitution


Are you sure its this? "int (1+x)/sqrt(x+x^2)"dx ?

I'm pretty sure you can't do it any other way. Substituting normal trig stuff won't do a thing. I'm 99% sure the question is wrong because I've done similar integrations in the further pure syllabus but not in core 3...

Reply 7
Avatar for andrewmc96
andrewmc96
2
Original post by tsumannai
Are you sure its this? "int (1+x)/sqrt(x+x^2)"dx ?

I'm pretty sure you can't do it any other way. Substituting normal trig stuff won't do a thing. I'm 99% sure the question is wrong because I've done similar integrations in the further pure syllabus but not in core 3...



I managed to get an equivalent answer to WolframAlpha using the subsitution x = (tan u)^2. But I'm not sure if this is part of the A Level syllabus as I'm studying Scottish Advanced Higher.
So this? 0.o

http://www3.wolframalpha.com/Calculate/MSP/MSP17291e9ia62545f68e92000032cfacagdidd7bbh?MSPStoreType=image/gif&s=31&w=392.&h=56.
Reply 9
Avatar for Notnek
Notnek
21
Original post by tsumannai
Are you sure its this? "int (1+x)/sqrt(x+x^2)"dx ?

I'm pretty sure you can't do it any other way. Substituting normal trig stuff won't do a thing. I'm 99% sure the question is wrong because I've done similar integrations in the further pure syllabus but not in core 3...


I'm 100% sure you can solve it with a trig substitution but I agree that it's not really a C3 integral.

Andrewmc96's method is better than mine.
(edited 10 years ago)
Ok I think it can be done using x=tan^2u done it sort of but its pretty long winded, not sure if it's right either xD

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you