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

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

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

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

\frac{1}{arccos ( x )} + C

Solution steps

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

Apply u-substitution

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

Take the constant out:

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

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

Apply the Power Rule

= - (- \frac{1}{u})

Substitute back

u = arccos (x)

= - (- \frac{1}{arccos ( x )})

Simplify

= \frac{1}{arccos ( x )}

Add a constant to the solution

= \frac{1}{arccos ( x )} + C

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