Square root integration problem

[kukumaluboy]

Homework Statement

Integrate : f(t) = t³/ sqrt(t²+1)

Homework Equations

The Attempt at a Solution

t²* t / sqrt(t²+1)let u = sqrt(t²+1)
u=(t²+1)^0.5
u² = t² +1
t² = u² -1 -Eq 1u=(t²-1)^0.5
du = t/sqrt(t²-1) dt
dt = sqrt(t²-1)/t du -Eq 2

Hence Substituting 1 and 2
Integrate : f(t)
= Integrate (u^2 -1) du

Is this way correct? If not can give me the right way

 

[HallsofIvy]

Looks good to me. I think I would have been inclined to use the simpler $u= t^2+ 1$, du= 2t dt so that t dt= (1/2)du and $t^2= u- 1$.

That would give
$$\int t^2\sqrt{t^2+ 1}dt= \int(u- 1)(\sqrt{u}(1/2)du= (1/2)\int u^{3/2}- u^{1/2}du$$
but that will give the same thing as your integral.

 

[kukumaluboy]

Alrite Thanks!