integral of (3x-1) / (sqrt (1-x^2)) dx

[math]

integral of (3x-1) / (sqrt (1-x^2)) dx


i know integral of 1 / sqrt (1 - x^2) is sin-1 (x) but what do I do with the 3x-1 ?

 

[galactus]

Try rewriting as:

\(\displaystyle \L\\3\int\frac{x}{\sqrt{1-x^{2}}}dx-\int\frac{1}{\sqrt{1-x^{2}}}dx\)

You know what the right integral is. Use a simple u-substitution on the left one.

Let \(\displaystyle \L\\u=x^{2}, \;\ \frac{du}{2}=xdx\)

 

[math]

thanks!