What is the integral of 5arccos(x) ?

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

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integral of 5arccos(x)

\int 5 arccos (x) d x

5 (x arccos (x) - 1 - x^{2}) + C

Solution steps

\int 5 arccos (x) d x

Take the constant out:

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

= 5 \cdot \int arccos (x) d x

Apply Integration By Parts

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

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

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

= 5 (x arccos (x) - 1 - x^{2})

Add a constant to the solution

= 5 (x arccos (x) - 1 - x^{2}) + C

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