What is the integral of arcsin(8x) ?

The integral of arcsin(8x) is xarcsin(8x)+1/8 sqrt(1-64x^2)+C

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integral of arcsin(8x)

\int arcsin (8 x) d x

x arcsin (8 x) + \frac{1}{8} 1 - 64 x^{2} + C

Solution steps

\int arcsin (8 x) d x

Apply Integration By Parts

: x arcsin (8 x) - \int \frac{8 x}{1 - 64 x ^{2}} d x

= x arcsin (8 x) - \int \frac{8 x}{1 - 64 x ^{2}} d x

\int \frac{8 x}{1 - 64 x ^{2}} d x = - \frac{1}{8} 1 - 64 x^{2}

= x arcsin (8 x) - (- \frac{1}{8} 1 - 64 x^{2})

Simplify

= x arcsin (8 x) + \frac{1}{8} 1 - 64 x^{2}

Add a constant to the solution

= x arcsin (8 x) + \frac{1}{8} 1 - 64 x^{2} + C

f (x) = x^{2} + x, at x = - 1, x = 2

(8.7) (- 6.7)

n = 1 \sum \infty \frac{3}{n ^{2} + 4}

\frac{1}{1 - a x}, 0

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

What is the integral of arcsin(8x) ?
The integral of arcsin(8x) is xarcsin(8x)+1/8 sqrt(1-64x^2)+C