# C3 Integration question HELP!!!Watch

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

0
5 years ago
#2
(Original post by HUBWD)
find the integral of 1+x/sqrt(x+x^2)

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#3
(Original post by notnek)
yea, it will be (1+x)/sqrt(x+x^2)
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5 years ago
#4
(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.
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5 years ago
#5
I don't think its possible, 1/(x+x^2)^1/2 requires hyperbolic substitution or something to be able to integrate it.
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5 years ago
#6
(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
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5 years ago
#7
(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...

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5 years ago
#8
(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.
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5 years ago
#9
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5 years ago
#10
(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.
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5 years ago
#11
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
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