Question

how do you integrate X/(sqrt(1-x^2)

Answer 1

use u-substitute.

let u = sqrt (1-x^2)

u^2 = 1 - x^2

2udu = 1 - 2xdx

since your numerator is just xdx...you isolate xdx

2xdx = 1 - 2udu

xdx = (1-2udu)/2

i assume you know the rest?

Answer 2

i'm actually helping out a friend who's in calc and i haven't done this for so long! could you please help me finish out the problem?

Answer 3

since xdx = (1-2udu)/2 and sqrt(1-x^2) is u then your integral becomes
\[\huge \int\frac{\frac{1-2udu}2}u\]
right?

Answer 4

okay got that

Answer 5

now take out that over two since it's just a coefficient \[\huge \frac 12\int \frac{1-2udu}u\]

Answer 6

then since the numerator is subtraction, you can separate the integrals
\[\huge \frac 12 [\int \frac 1u du - \int \frac{2udu}u]\]
do you now know the rest?

Answer 7

yeah i got it from there! thanks so much for the help!

Answer 8

You also could have made the substitution
\[u=1-x^2~\Rightarrow~-\frac{1}{2}du=x~dx\]
(same thing as @roxygurl453's suggestion, really) or a trigonometric substitution.

Answer 9

Sorry, meant @abb50!

Answer 10

ohhh okay haha thanks ! i appreciate the help a lot !!!!