What is the integral of-3arcsin(10x) ?

The integral of-3arcsin(10x) is -3(xarcsin(10x)+1/10 sqrt(1-100x^2))+C

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integral of-3arcsin(10x)

\int - 3 arcsin (10 x) d x

- 3 (x arcsin (10 x) + \frac{1}{10} 1 - 100 x^{2}) + C

Solution steps

\int - 3 arcsin (10 x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - 3 \cdot \int arcsin (10 x) d x

Apply Integration By Parts

: x arcsin (10 x) - \int \frac{10 x}{1 - 100 x ^{2}} d x

= - 3 (x arcsin (10 x) - \int \frac{10 x}{1 - 100 x ^{2}} d x)

\int \frac{10 x}{1 - 100 x ^{2}} d x = - \frac{1}{10} 1 - 100 x^{2}

= - 3 (x arcsin (10 x) - (- \frac{1}{10} 1 - 100 x^{2}))

Simplify

= - 3 (x arcsin (10 x) + \frac{1}{10} 1 - 100 x^{2})

Add a constant to the solution

= - 3 (x arcsin (10 x) + \frac{1}{10} 1 - 100 x^{2}) + C

(- 5, - 2), (5, 4)

\int arcsin (x) x d x

x \to - 3 lim (2 x^{3} + 5 x^{2} - 25)

y^{^{'}} = \frac{2 y}{x}, y (1) = 2

\int_{0}^{1} \frac{x}{e ^{2 x}} d x

What is the integral of-3arcsin(10x) ?
The integral of-3arcsin(10x) is -3(xarcsin(10x)+1/10 sqrt(1-100x^2))+C