Question

anti derivative of (x+1)/ (sqrt (1-x^2))

Answer 1

note that \(\frac{d}{dx} \sqrt{1-x^2} = \frac{1}{2} (1-x^2)^{-\frac{1}{2}}(-2x) = ???\)

with a bit of fiddling, that deals with first part of the integrand's numerator

for the other part of the numerator, you should try *the* trig sub

Answer 2

can you walk me through that or just do it so i can see it

Answer 3

nah, there's only so much i can do before I get another email saying i did someone's work for them.....:-(

but we/you can tidy this up.....
\[\frac{d}{dx} \sqrt{1-x^2} = \frac{1}{2} (1-x^2)^{-\frac{1}{2}}(-2x) = \dfrac{-x}{\sqrt{1-x^2}}\]

and you are integrating \(\dfrac{\color{red}{x}+1}{\sqrt {1-x^2}}\)

you really should now see what you are left with.

good luck!! if no-one helps you, tag me....