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

Popular >

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

= \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}

= - (- \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

\int x^{2} (4 - x^{2}) d x

\int \frac{sin ^{3} ( x ) + 1}{sin ^{2} ( x )} d x

\int \frac{4}{x ( x ^{2} + 4 )} d x

\int 45 + 4 x d x

\int 2 x sin (5 x) d x

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