C3 Integration question HELP!!! Watch

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

how would you go about answering that question ?
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Notnek
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(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.
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HUBWD
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(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)
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Notnek
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(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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tsumannai
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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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andrewmc96
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(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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tsumannai
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(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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andrewmc96
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(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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tsumannai
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So this? 0.o

http://www3.wolframalpha.com/Calcula...1&w=392.&h=56.
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Notnek
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(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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tsumannai
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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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