integration problem... i can't figure it out?

This is the same as sqrt(t^2) * sqrt(1 + t^2) = t * sqrt(1 + t^2)

Let u = 1 + t^2

Then du = 2t dt and t dt = du/2

So we have ∫ u^(1/2) du/2 = (u^(3/2) / (3/2)) * (1/2) + C =

(u^(3/2)) * (2/3) * (1/2) + C = (1/3) * (u^(3/2)) + C

But u was defined as 1 + t^2, so the answer is:

(1/3) * ((1 + t^2)^(3/2)) + C <------------ Answer

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sqrt(t^2+t^4)=tsqrt(t^2+1)

integrate = (1/3) (t^2+1)^(3/2) + c