What is the integral of 6arccos(5x) ?

The integral of 6arccos(5x) is 6(xarccos(5x)-1/5 sqrt(1-25x^2))+C

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integral of 6arccos(5x)

\int 6 arccos (5 x) d x

6 (x arccos (5 x) - \frac{1}{5} 1 - 25 x^{2}) + C

Solution steps

\int 6 arccos (5 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 (5 x) d x

Apply Integration By Parts

: x arccos (5 x) - \int - \frac{5 x}{1 - 25 x ^{2}} d x

= 6 (x arccos (5 x) - \int - \frac{5 x}{1 - 25 x ^{2}} d x)

\int - \frac{5 x}{1 - 25 x ^{2}} d x = \frac{1}{5} 1 - 25 x^{2}

= 6 (x arccos (5 x) - \frac{1}{5} 1 - 25 x^{2})

Add a constant to the solution

= 6 (x arccos (5 x) - \frac{1}{5} 1 - 25 x^{2}) + C

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What is the integral of 6arccos(5x) ?
The integral of 6arccos(5x) is 6(xarccos(5x)-1/5 sqrt(1-25x^2))+C