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

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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

= 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

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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