Question

How can I integrate please: x/sqrt(1-x^2)

Answer 1

consider a substitution? u = 1-x^2

or a trig sub? x = sin

Answer 2

if x = sin, dx = cos dt

sin cos
------------ dt
sqrt(1-sin^2)


sin cos
------------ dt
cos


sin dt

Answer 3

thanks amistre. You're wonderful!

Answer 4

How do you recognise when to use a trig sub? Do I just need to do a lot more practice?

Answer 5

practice helps alot, the usub would have worked too

u = 1-x^2

du = -2x dx

-du/2 = x dx

integrate -1/2sqrt(u) du = -sqrt(u) is the same resutls