Integration help

  • Thread starter cragar
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  • #1
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Homework Statement


Integral of 1/(x^2+sqrt(x)) dx

The Attempt at a Solution



i tried u=sqrt(x)
so then 2udu=dx
u^2=x

so then 2 integral u/(u^4+u) du

then integral 2/(u^3+1)du then i factored it with sum of cubes then i did partial fraction's
on it is this the right approach.
 

Answers and Replies

  • #2
Dick
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Seems fine to me so far.
 
  • #3
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but when i do the partial fractions after i factor the sum of cubes i get an unfactorable quadratic and i can't get the terms to cancel out with out the other cancilind out to find out the leading co-effiecients of the numertors of the partial fractions.
 
  • #4
Dick
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Yes, you do get an irreducible quadratic. Complete the square in the denominator and use a trig substitution.
 
  • #5
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we havn't learned trig substitution yet.
 
  • #6
Dick
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I guess I don't see any other way to do it. There's an arctan in there I don't see how to get around.
 
  • #7
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ok this wasn't a required problem my teacher said some of us could maybe do it
so ill just wait till we learn trig sub.
 

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