What is the integral of 2/pi arcsin(x-1)+1 ?

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

integral of 2/pi arcsin(x-1)+1

\int \frac{2}{π} arcsin (x - 1) + 1 d x

x (\frac{2}{π} arcsin (x - 1) + 1) - \frac{2}{π} (- - x^{2} + 2 x + arcsin (x - 1)) + C

Solution steps

\int \frac{2}{π} arcsin (x - 1) + 1 d x

Apply Integration By Parts

= x (\frac{2}{π} arcsin (x - 1) + 1) - \int \frac{2 x}{π - x ^{2} + 2 x} d x

\int \frac{2 x}{π - x ^{2} + 2 x} d x = \frac{2}{π} (- - x^{2} + 2 x + arcsin (x - 1))

= x (\frac{2}{π} arcsin (x - 1) + 1) - \frac{2}{π} (- - x^{2} + 2 x + arcsin (x - 1))

Add a constant to the solution

= x (\frac{2}{π} arcsin (x - 1) + 1) - \frac{2}{π} (- - x^{2} + 2 x + arcsin (x - 1)) + C

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