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

The integral of arcsin(2x+2) is xarcsin(2x+2)+1/2 sqrt(-4x^2-8x-3)+arcsin(2(x+1))+C

integral of arcsin(2x+2)

\int arcsin (2 x + 2) d x

x arcsin (2 x + 2) + \frac{1}{2} - 4 x^{2} - 8 x - 3 + arcsin (2 (x + 1)) + C

Solution steps

\int arcsin (2 x + 2) d x

Apply Integration By Parts

= x arcsin (2 x + 2) - \int \frac{2 x}{- 4 x ^{2} - 8 x - 3} d x

\int \frac{2 x}{- 4 x ^{2} - 8 x - 3} d x = - \frac{1}{2} - 4 x^{2} - 8 x - 3 - arcsin (2 (x + 1))

= x arcsin (2 x + 2) - (- \frac{1}{2} - 4 x^{2} - 8 x - 3 - arcsin (2 (x + 1)))

Simplify

= x arcsin (2 x + 2) + \frac{1}{2} - 4 x^{2} - 8 x - 3 + arcsin (2 (x + 1))

Add a constant to the solution

= x arcsin (2 x + 2) + \frac{1}{2} - 4 x^{2} - 8 x - 3 + arcsin (2 (x + 1)) + C

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

\int \frac{1}{x ^{2}} + 3 d x

\int \frac{x}{2 + 3 x ^{2}} d x

\int e^{- z} d z

\int \frac{x ^{2}}{x ^{2} + 3 x + 2} d x

What is the integral of arcsin(2x+2) ?
The integral of arcsin(2x+2) is xarcsin(2x+2)+1/2 sqrt(-4x^2-8x-3)+arcsin(2(x+1))+C