What is the integral of-6arccos(3x) ?

The integral of-6arccos(3x) is -6(xarccos(3x)-1/3 sqrt(1-9x^2))+C

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integral of-6arccos(3x)

\int - 6 arccos (3 x) d x

- 6 (x arccos (3 x) - \frac{1}{3} 1 - 9 x^{2}) + C

Solution steps

\int - 6 arccos (3 x) d x

Take the constant out:

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

= - 6 \cdot \int arccos (3 x) d x

Apply Integration By Parts

= - 6 (x arccos (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}

= - 6 (x arccos (3 x) - \frac{1}{3} 1 - 9 x^{2})

Add a constant to the solution

= - 6 (x arccos (3 x) - \frac{1}{3} 1 - 9 x^{2}) + C

What is the integral of-6arccos(3x) ?
The integral of-6arccos(3x) is -6(xarccos(3x)-1/3 sqrt(1-9x^2))+C