Integral of 1/(x^2+sqrt(x)) - Step by Step Solution

[cragar]

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.

 

[Dick]

Seems fine to me so far.

 

[cragar]

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 without the other cancilind out to find out the leading co-effiecients of the numertors of the partial fractions.

 

[Dick]

Yes, you do get an irreducible quadratic. Complete the square in the denominator and use a trig substitution.

 

[cragar]

we havn't learned trig substitution yet.

 

[Dick]

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.

 

[cragar]

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.