What is the integral of arcsin(x-1) ?

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

Popular >

integral of arcsin(x-1)

\int arcsin (x - 1) d x

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

Solution steps

\int arcsin (x - 1) d x

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

\int (3 csc (3 x) + 2 cot (3 x))^{2} d x

\int \frac{2 + sin ^{2} ( x )}{cos ^{2} ( x )} d x

\int \frac{y}{( y ^{2} + 1 )} d y

\int \frac{1}{x ( 1 + 3 ln ( x ) )} d x

\int \frac{3 x}{x} d x

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