how do you integrate dx/(x^2*(x^2+4)^1/2)?
To integrate dx/(x^2*(x^2+4)^(1/2)), you can use the method of substitution. Follow these steps:
1. Let's start by making a substitution. Let u = x^2 + 4. We can then rewrite the integral as dx/(x^2*(x^2+4)^(1/2)) = (1/2) * du/u^(1/2)
2. Now, we can rewrite the integral in terms of "u" as follows: (1/2) * ∫ du/u^(1/2)
3. Next, we can simplify the integral by bringing the exponent down and integrating the simplified form: (1/2) * ∫ u^(-1/2) du
4. Integrate u^(-1/2) with respect to u, which results in (1/2) * (2u^(1/2))
5. Simplify: u^(1/2) = √(x^2 + 4)
6. Finally, remember to undo the substitution by replacing u with its equivalent expression in terms of x: (1/2) * (2u^(1/2)) = √(x^2 + 4)
So, the final answer to the integral is √(x^2 + 4) + C, where C is the constant of integration.