The problem is ∫ x⁵/√ (1+x³). I took 1+x³ = t².

I am supposed to get 2/3∫t(t²-1)/√t but what I get is2/3 ∫t(t²-1)/ t.. How did that square root "t" pop out? If 1+x³ = t² then,

√(1+x³) would be √t² after cancelling the root then we get t. How am I suppose to get that square root "t" as the denominator? I am terribly lost.

I am a bit lost - but it may help you and the other members if you are a bit more explicit in each of your stages. Ignoring the integral and other bit I would think that your term "2/3 ∫t(t²-1)/ t"

 

[math] \frac{t(t^2-1)}{t} = t^2-1[/math]

 

No matter what is around it the lone t in the denominator and numerator can cancel out. That would leave you (subbing back in to double check) with an x term in the order of x^6 which is clearly incorrect.

 

I think you may find your problem in what you are doing to express the numerator in terms of t