Find the integral integral xsqrt(1-x2)\,dx and select the correct option.

Let $u = 1-x^2$.

Differentiate $u$ with respect to $x$:

Rearrange to find $x\,dx$:

Replace $1-x^2$ with $u$ and $x\,dx$ with $-\frac{1}{2}\,du$:

Use the power rule for integration, $\int u^n\,du = \frac{u^{n+1}}{n+1} + C$:

Replace $u$ with $1-x^2$:

Comparing this result with the given options, it matches option B.

The final answer is $\text{B: } -\frac{1}{3}(1-x^2)^{3/2} + c$.