What is the integral of (arccos(x)-ln(x)) ?

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

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integral of (arccos(x)-ln(x))

\int (arccos (x) - ln (x)) d x

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

Solution steps

\int arccos (x) - ln (x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int arccos (x) d x - \int ln (x) d x

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

\int ln (x) d x = x ln (x) - x

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

Simplify

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

Add a constant to the solution

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

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