Find primitives of function (1+4x)/sqrt(1 + x + 2x^2)

  • Thread starter Taryn
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  • #1
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This is a practice exam question that I have been given!
Find the primitives of the functions
(1+4x)/(sqrt(1+x+2x^2))

My question is 1. is a primitive the antiderivative? I dont remember my lecturer using primitive during our course!
 

Answers and Replies

  • #2
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It is basically asking you to find:

[tex] \int \frac{1+4x}{\sqrt{1+x+2x^{2}}} \; dx [/tex]

A primitive is an antiderivative.

So set [tex] u = 1+x+2x^{2} [/tex]

Then [tex] du = 4x+1 \; dx [/tex] and you end up with [tex] \int u^{-\frac{1}{2}} \; du [/tex]. All the primitives mean that you add the integration constant [tex] C [/tex].
 
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  • #3
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ahhh thanks!
 

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