How to integrate this? With steps please.

>>8288987
use integration by parts and good luck
>I'll give you the first step; set u equal to the inverse trigonometric function, and let dv equal to the differential

>>8288987
try substituting x with tan^2 theta

>>8288987
(1-x)/(1+x) with arctg looks very familiar to me.

Just look up your books m8, it obviously look easy

symbolab.com

>>8289200
>[math]\mathrm{Steps\:are\:currently\:not\:supported\:for\:this\:problem}[/math]

>>8289209
Cool font m8

>>8289211
[math]\color{#dd3625}{\text{T}}\color{#e04c29}{\text{h}}\color{#e3612d}{\text{a}}\color{#e67531}{\text{n}}\color{#e58634}{\text{k}}\color{#e49637}{\text{s}}[/math] [math]\color{#d9ac3d}{\text{i}}\color{#d0b340}{\text{t}}[/math] [math]\color{#bbbb49}{\text{a}}\color{#aebd4f}{\text{l}}\color{#a2bd57}{\text{s}}\color{#95bc60}{\text{o}}[/math] [math]\color{#7db876}{\text{c}}\color{#72b484}{\text{o}}\color{#68af91}{\text{m}}\color{#5fa99f}{\text{e}}\color{#57a1ac}{\text{s}}[/math] [math]\color{#4a8cc2}{\text{i}}\color{#457fca}{\text{n}}[/math] [math]\color{#3e5fcf}{\text{r}}\color{#3e4dcb}{\text{a}}\color{#3f3bc4}{\text{i}}\color{#462db8}{\text{n}}\color{#4e1eaa}{\text{b}}\color{#631c98}{\text{o}}\color{#781b86}{\text{w}}[/math]

>>8288987
change variables

>>8289216
kek

>>8289144
cant do that, x can be negative

>>8288996
no inverse trig will help you here, it should be integrated by parts though

>>8289169
the integration of root(1-x/1+x) is a common problem but that wont help you here

Integrate by parts so that the problem is solved with the integral of fg, where f is x and g is the derivative of arctanroot(1-x/1+x), the rest is algebra.

Multiply the inside of the parentheses by sqrt(1-x)/sqrt(1-x). It becomes (1-x)/sqrt(1-x^2). Then try u substitution.