Another partial fraction question, this time they gave me int 1/(x^2+xsqrt(x))dx, how do I do it when I only have a constant on top but nothing that would give me a constant on the bottom?

Question

anonymous · Answer

In equation form: $$\int\limits_{}^{}\frac{ 1 }{ x^2+x \sqrt{x} }dx$$

hartnn · Answer

lets simplify this by first substituting sqrt x as y 

so whats 
x^2 =... ?
x\sqrt x = ... ?

anonymous · Answer

I'm sorry, I'm still lost by that

hartnn · Answer

$\sqrt x=y$
square both sides, what u get ?

anonymous · Answer

x=y^2

hartnn · Answer

right
so, x^2 = ... ?

anonymous · Answer

y^4, but im not seeing how this is helping yet because there's still a dx in the equation

hartnn · Answer

right,
that will help only for partial fractions part!

so we have 
y^4 + y^3 in the denominator right ?? 
which is y^3 (1+y)

can u do partial fractions for this ?

hartnn · Answer

in the end, just replace back,
y =sqrt x

anonymous · Answer

yeah but if i did the substitution like you're suggesting now i'd have $$\int\limits_{}^{}\frac{ 1 }{ y^4+y^3 }dx$$ and you can't mix variables so what happens to the dx?

anonymous · Answer

oh wait you mean just use the y to simplify the algebra and then sub back in with the dx, i get it now

hartnn · Answer

as i just said, use it for partial only

forget about the integral and dx for now

hartnn · Answer

yes yes!