int dx / sqrt(1-(x+1)^2) Find the indefinite integral

Indefinite integral are written in the form of int f(x) dx = F(x) +C
 where: f(x) as the integrand
           F(x) as the anti-derivative function 
           C  as the arbitrary constant known as constant of integration
 
For the given problem, the integrand f(x) =1/sqrt(1 -(x+1)^2)  we apply
u-substitution by letting u =(x+1)  and du = 1 dx or du= dx .
int (dx)/sqrt(1 -(x+1)^2) = int (du)/sqrt(1 -u^2)
 
int (du)/sqrt(1 -u^2)   resembles the basic integration formula for inverse sine function: int (dx)/sqrt(1-x^2)=arcsin(x) +C .
By applying the formula, we get:
int (du)/sqrt(1 -u^2) =arcsin(u) +C
Then to express it in terms of x, we substitute u=(x+1) :
arcsin(u) +C =arcsin(x+1) +C
 

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