What is the integral of arcsin(u) ?

The integral of arcsin(u) is uarcsin(u)+sqrt(1-u^2)+C

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integral of arcsin(u)

\int arcsin (u) d u

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

Solution steps

\int arcsin (u) d u

Apply Integration By Parts

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

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

\int \frac{u}{1 - u ^{2}} d u = - 1 - u^{2}

= u arcsin (u) - (- 1 - u^{2})

Simplify

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

Add a constant to the solution

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

\int_{0}^{x} 1 d x

\frac{d}{d x} ((5 x + 1)^{2})

f (θ) = 3 sec (θ)

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

(5, 6), (3, 4)

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