What is the integral of arcsin(t) ?

The integral of arcsin(t) is tarcsin(t)+sqrt(1-t^2)+C

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integral of arcsin(t)

\int arcsin (t) d t

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

Solution steps

\int arcsin (t) d t

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

\frac{\partial}{\partial x} (2 x^{2} - 5 y^{2})

\int_{- 2}^{6} 4 x - x^{2} + 12 d x

\int_{5}^{7} [\frac{k}{2} x^{2}] d x

y^{^{''}} + 5 y^{^{'}} = e^{- t}, y (0) = 0, y^{^{'}} (0) = 1

\frac{\partial}{\partial y} (e^{x y} ln (z))

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