What is the integral of arcsin(x/4) ?

The integral of arcsin(x/4) is xarcsin(x/4)+sqrt(16-x^2)+C

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integral of arcsin(x/4)

\int arcsin (\frac{x}{4}) d x

x arcsin (\frac{x}{4}) + 16 - x^{2} + C

Solution steps

\int arcsin (\frac{x}{4}) d x

Apply Integration By Parts

: x arcsin (\frac{x}{4}) - \int \frac{x}{16 - x ^{2}} d x

= x arcsin (\frac{x}{4}) - \int \frac{x}{16 - x ^{2}} d x

\int \frac{x}{16 - x ^{2}} d x = - 16 - x^{2}

= x arcsin (\frac{x}{4}) - (- 16 - x^{2})

Simplify

= x arcsin (\frac{x}{4}) + 16 - x^{2}

Add a constant to the solution

= x arcsin (\frac{x}{4}) + 16 - x^{2} + C

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What is the integral of arcsin(x/4) ?
The integral of arcsin(x/4) is xarcsin(x/4)+sqrt(16-x^2)+C