Integral Help: 1/((4x^2)+(4x)+5)

[tmclary]

Homework Statement

Integrate the indefinite integral of 1/((4x^2)+(4x)+5)

Homework Equations

The Attempt at a Solution

 

[Hootenanny]

Homework Statement

Integrate the indefinite integral of 1/((4x^2)+(4x)+5)

I assume you mean find the indefinite integral. You also forgot to fill in the following two sections, in particular the final one:

The Attempt at a Solution

 

[tmclary]

Sorry, I have no clue how to get started. The denominator won't factor (at least to linear factors w/ integral coefficients) and the discriminant is complex anyway. So if it's a partial fraction type solution, how do you get started? Thanks.

 

[Defennder]

Try completing the square of the denominator.

 

[tmclary]

So 1/(4x^2)+4x+5 =1/((2x+1)^2)+4 and I make a u-sub. Looks like tan^-1 type integral. Correct?

 

[Hootenanny]

So 1/(4x^2)+4x+5 =1/((2x+1)^2)+4 and I make a u-sub. Looks like tan^-1 type integral. Correct?

Looks good to me . Choose your substitution carefully.

 

[tmclary]

Thanks for your help, Def & Hoot!

 

[Hootenanny]

Thanks for your help, Def & Hoot!

A pleasure

 

[m_s_a]

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