Learn how to solve problems step by step online. Find the integral int((s^2)/((100+s^2)^(1/2)^3))ds. Simplify \left(\sqrt{100+s^2}\right)^3 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals \frac{1}{2} and n equals 3. We can solve the integral \int\frac{s^2}{\sqrt{\left(100+s^2\right)^{3}}}ds by applying integration method of trigonometric substitution using the substitution. Now, in order to rewrite d\theta in terms of ds, we need to find the derivative of s. We need to calculate ds, we can do that by deriving the equation above. Substituting in the original integral, we get.

Find the integral int((s^2)/((100+s^2)^(1/2)^3))ds