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

The integral of 3arcsin(3x) is 3xarcsin(3x)+sqrt(1-9x^2)+C

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integral of 3arcsin(3x)

\int 3 arcsin (3 x) d x

3 x arcsin (3 x) + 1 - 9 x^{2} + C

Solution steps

\int 3 arcsin (3 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 (3 x) d x

Apply Integration By Parts

: x arcsin (3 x) - \int \frac{3 x}{1 - 9 x ^{2}} d x

= 3 (x arcsin (3 x) - \int \frac{3 x}{1 - 9 x ^{2}} d x)

\int \frac{3 x}{1 - 9 x ^{2}} d x = - \frac{1}{3} 1 - 9 x^{2}

= 3 (x arcsin (3 x) - (- \frac{1}{3} 1 - 9 x^{2}))

Simplify

3 (x arcsin (3 x) - (- \frac{1}{3} 1 - 9 x^{2})) : 3 x arcsin (3 x) + 1 - 9 x^{2}

= 3 x arcsin (3 x) + 1 - 9 x^{2}

Add a constant to the solution

= 3 x arcsin (3 x) + 1 - 9 x^{2} + C

\frac{d}{d x} (lo g_{5} (1 + 2 x))

\frac{d}{d x} (\frac{x ^{\frac{1}{3}} - 4}{x ^{\frac{7}{2}}})

x \to 0 lim (x \cdot co tan (2 π x))

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

y^{^{''}} + 9 y = 0

What is the integral of 3arcsin(3x) ?
The integral of 3arcsin(3x) is 3xarcsin(3x)+sqrt(1-9x^2)+C