Question

Help me finish evaluating this integral

Answer 1

Okay I am working on the following \[\int\limits_{}^{}\sin^{-1} x dx\] and I am using integration by parts setting u = arcsin(x) and dv = dx and du = \[\frac{ xdx }{ \sqrt{1^2-x^2} }\] and v = x

Answer 2

so now I am left with the following

Answer 3

\[s \sin^{-1} x - \int\limits_{}^{}\frac{ x dx }{ \sqrt{1^2 - x^2} }\]

Answer 4

that "s" is an "x"

Answer 5

now I need help integrating that trig identity on the right. I think its sine

Answer 6

would I integrate the right side like this arcsin(x) + c?

Answer 7

oh no trig identity
basic u sub will do
try \(u=1-x^2\)

Answer 8

okay let me see

Answer 9

oh wait doh nvm

Answer 10

your method is correct, just use a u sub

Answer 11

then simple u sub
u = 1 - x^2
du = 2x dx
1/2x du = dx

Answer 12

wait isn't that a -1/2