# Square root integration problem

## Homework Statement

Integrate : f(t) = t3/ sqrt(t2+1)

## 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 1

u=(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
Homework Helper

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.

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Alrite Thanks!!