What is the integral of arcsin(x+2) ?

The integral of arcsin(x+2) is xarcsin(x+2)+sqrt(-x^2-4x-3)+2arcsin(x+2)+C

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integral of arcsin(x+2)

\int arcsin (x + 2) d x

x arcsin (x + 2) + - x^{2} - 4 x - 3 + 2 arcsin (x + 2) + C

Solution steps

\int arcsin (x + 2) d x

Apply Integration By Parts

= x arcsin (x + 2) - \int \frac{x}{- x ^{2} - 4 x - 3} d x

\int \frac{x}{- x ^{2} - 4 x - 3} d x = - - x^{2} - 4 x - 3 - 2 arcsin (x + 2)

= x arcsin (x + 2) - (- - x^{2} - 4 x - 3 - 2 arcsin (x + 2))

Simplify

= x arcsin (x + 2) + - x^{2} - 4 x - 3 + 2 arcsin (x + 2)

Add a constant to the solution

= x arcsin (x + 2) + - x^{2} - 4 x - 3 + 2 arcsin (x + 2) + C

What is the integral of arcsin(x+2) ?
The integral of arcsin(x+2) is xarcsin(x+2)+sqrt(-x^2-4x-3)+2arcsin(x+2)+C