Mastering Trig Substitution for Evaluating Integrals of 1/x(4x+1)^1/2 in Calc II

[GravityGirl]

evaluate the integral of 1/x(4x+1)^1/2

so what i am thinking is that i will have to use a trig substution some how for
4x+1

maybe x=secu since the substution for a^2+x^2=sec^2u

but i am not sure how to go ahead and do it

please help me

 

[Dick]

No. Don't do trig. Try u^2=4*x+1. You'll get a simple rational function you can then do with partial fractions.

 

[VietDao29]

evaluate the integral of 1/x(4x+1)^1/2

so what i am thinking is that i will have to use a trig substution some how for
4x+1

maybe x=secu since the substution for a^2+x^2=sec^2u

but i am not sure how to go ahead and do it

please help me

Well, as Dick pointed out, you should let $$u = \sqrt{4x + 1}$$
Or, in general, if you meet some radical, then it's common to let u = that whole radical, and then go from there.

You only let x = sec(u), when you meet: $$\sqrt{x ^ 2 - 1}$$, or when encountering $$\sqrt{x ^ 2 - a ^ 2}$$, you then let x = a sec(u).

Can you go from here? :)

 

[Gib Z]

I guess if she really wanted to, she could have done x= 1/4 tan^2 u. Takes much much longer though.