What is the integral of 1/(sqrt(1-x^2)arccos(x)) ?

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

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integral of 1/(sqrt(1-x^2)arccos(x))

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

- ln ∣ arccos (x) ∣ + C

Solution steps

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

Apply u-substitution

= \int - \frac{1}{u} d u

Take the constant out:

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

= - \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - ln ∣ u ∣

Substitute back

u = arccos (x)

= - ln ∣ arccos (x) ∣

Add a constant to the solution

= - ln ∣ arccos (x) ∣ + C

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