Integrating Using Arctan: Solving for the Integral of 1/(x^2+11x+29)

[jumbogala]

Homework Statement

Integrate
1/(x² +11x +29)

Homework Equations

The Attempt at a Solution

I'm doing something wrong, but can't figure out what...

Complete the square so that the denominator equals (x+2)²+25

Then divide by 25: ((x+2)²)/25 + 1

Move that 25 into the squared part: ((x+2)/5)²+1

Substitute the squared part for u.

Find du/dx = 1/5, and therefore 5du=dx

Now we have 5*(integral sign) du / (u²+1)

This gives 5arctan(u)+C --> substitute u back for what you had before.

But the answer is 1/5arctan(u). Where did I go wrong?

 

[NoMoreExams]

When you "divide by 25", where does that 25 go?

 

[jumbogala]

Oops, I was focusing so much on the denominator, I forgot about the numerator. This is what happens when yiou do math late at night, haha.

Thanks!

 

[Dick]

You can't just divide by something and expect the answer to be unchanged. Once you have 1/((x+5)^2+25) why not just substitute (x+5)=5*u?

 

[djeitnstine]

how about x+2 = 5tanu to make life easier