integration with substitution Watch

FPL67
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Report Thread starter 8 years ago
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Hi

i have to do integration with substitution, i have tried a few substitutions but none seem to work, could someone please give me a hint on what it could be

Integral from 1 to 2 of (4x + 6) / (x^2 + 3x + 5 )

thanks
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sonofdot
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What do you get if you differentiate the denominator of the fraction? Can you see how this is helpful?
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Galadirith
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Hey FPL67, well lets see then.

Well I dont actually think this is easiest done with a substitution. Does it actually say you have to use one or is that what you have figured would be best. As a side note, one often likes to think of subtitutions as universal integral solvers, which certainly isnt the case so you should always be mindful of other integral stratagies ;D.

That said, first have a look at x^2 + 3x + 5,

\displaystyle \frac{d}{dx}\left( x^2 + 3x + 5 \right) = 2x + 3
and

4x+6 = 2(2x+3)

Now with that info, have a careful think about the integral, this boils down to a simple matter of manipulating coefficients to lead to a direct integral, what standard integral do you know where its a derived function over its function.

If you absolutly have to use a substitution, then this can be taken further, investigate the completed square of the quadratic denominator, can you do some manipulation of coefficients here to, and spot a simple subtitution ;D.
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steve2005
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(Original post by Galadirith)
Hey FPL67, well lets see then.

Well I dont actually think this is easiest done with a substitution. Does it actually say you have to use one or is that what you have figured would be best. As a side note, one often likes to think of subtitutions as universal integral solvers, which certainly isnt the case so you should always be mindful of other integral stratagies ;D.

That said, first have a look at x^2 + 3x + 5,

\displaystyle \frac{d}{dx}\left( x^2 + 3x + 5 \right) = 2x + 3
and

4x+6 = 2(2x+3)

Now with that info, have a careful think about the integral, this boils down to a simple matter of manipulating coefficients to lead to a direct integral, what standard integral do you know where its a derived function over its function.

If you absolutly have to use a substitution, then this can be taken further, investigate the completed square of the quadratic denominator, can you do some manipulation of coefficients here to, and spot a simple subtitution ;D.
A simple substitution works just fine.
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