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

[Taryn]

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 don't remember my lecturer using primitive during our course!

 

[courtrigrad]

It is basically asking you to find:

$$\int \frac{1+4x}{\sqrt{1+x+2x^{2}}} \; dx$$

A primitive is an antiderivative.

So set $$u = 1+x+2x^{2}$$

Then $$du = 4x+1 \; dx$$ and you end up with $$\int u^{-\frac{1}{2}} \; du$$. All the primitives mean that you add the integration constant $$C$$.

 

[Taryn]

ahhh thanks!