What is the integral of 1/(sqrt(1-(x-1)^2)) ?

The integral of 1/(sqrt(1-(x-1)^2)) is arcsin(x-1)+C

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integral of 1/(sqrt(1-(x-1)^2))

\int \frac{1}{1 - ( x - 1 ) ^{2}} d x

arcsin (x - 1) + C

Solution steps

\int \frac{1}{1 - ( x - 1 ) ^{2}} d x

Apply u-substitution

= \int \frac{1}{1 - u ^{2}} d u

Use the common integral:

\int \frac{1}{1 - u ^{2}} d u = arcsin (u)

= arcsin (u)

Substitute back

u = x - 1

= arcsin (x - 1)

Add a constant to the solution

= arcsin (x - 1) + C

What is the integral of 1/(sqrt(1-(x-1)^2)) ?
The integral of 1/(sqrt(1-(x-1)^2)) is arcsin(x-1)+C