What is the integral from 0 to x of arcsin(t) ?

The integral from 0 to x of arcsin(t) is xarcsin(x)+sqrt(1-x^2)-1

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integral from 0 to x of arcsin(t)

\int_{0}^{x} arcsin (t) d t

x arcsin (x) + 1 - x^{2} - 1

Solution steps

\int_{0}^{x} arcsin (t) d t

Apply Integration By Parts

: [t arcsin (t) - \int \frac{t}{1 - t ^{2}} d t]_{0}^{x}

= [t arcsin (t) - \int \frac{t}{1 - t ^{2}} d t]_{0}^{x}

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

= [t arcsin (t) - (- 1 - t^{2})]_{0}^{x}

Simplify

= [t arcsin (t) + 1 - t^{2}]_{0}^{x}

Compute the boundaries:

x arcsin (x) + 1 - x^{2} - 1

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

\int_{2}^{3} - \frac{3}{x ^{2}} d x

\int_{1}^{2} (x^{3} + 4) d x

\int_{0}^{1} 3 x^{2} (4 x^{3} - 5)^{3} d x

\int_{0}^{3} (x^{2} + 1)^{2} d x

\int_{1}^{e} \frac{x ^{2} + 1}{2 x} d x

What is the integral from 0 to x of arcsin(t) ?
The integral from 0 to x of arcsin(t) is xarcsin(x)+sqrt(1-x^2)-1