Re: Integration Inverse trig
Do you understand how substitution works? You need to see if there is an "inner" function and if this inner function's derivative is a factor in your integrand. Surely you can see that [math]\displaystyle \begin{align*} x = \left( \sqrt{x} \right) ^2 \end{align*}[/math]. Why did we choose to do that? Because if you know your derivatives, you will know that [math]\displaystyle \begin{align*} \frac{d}{dx} \left( \sqrt{x} \right) = \frac{1}{2\sqrt{x}} \end{align*}[/math]. Notice that you ALREADY have [math]\displaystyle \begin{align*} \frac{1}{\sqrt{x}} \end{align*}[/math] in your denominator, which means that if you can turn it into [math]\displaystyle \begin{align*} \frac{1}{2\sqrt{x}} \end{align*}[/math], then a substitution of the form [math]\displaystyle \begin{align*} u = \sqrt{x} \end{align*}[/math] is appropriate.