s(t) = the integral (from 1 to sqrt of t) sqrt of (1 x^2)dx

I suppose that "1 x^2" means "1/x^2". If not please tell and I'll re-solve.

Indefinite integral is ln(x). We have to substitute x from 1 to sqrt(t), obtain

ln(sqrt(t)) - 0 = (1/2)*ln(t).

Will be different if (1 + x^2) or (1 - x^2).

For sqrt(1-x^2) integral is (1/2)(x*sqrt(1-x^2) + arcsin(x)).

For sqrt(1+x^2) is (1/2)*(x*sqrt(1+x^2) + arcsinh(x)).

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