What is the integral of 1/((arcsin(x))^3sqrt(1-x^2)) ?

The integral of 1/((arcsin(x))^3sqrt(1-x^2)) is -1/(2arcsin^2(x))+C

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integral of 1/((arcsin(x))^3sqrt(1-x^2))

\int \frac{1}{( arcsin ( x ) ) ^{3} 1 - x ^{2}} d x

- \frac{1}{2 arcsin ^{2} ( x )} + C

Solution steps

\int \frac{1}{( arcsin ( x ) ) ^{3} 1 - x ^{2}} d x

Simplify

= \int \frac{1}{arcsin ^{3} ( x ) 1 - x ^{2}} d x

Apply u-substitution

: \int \frac{1}{u ^{3}} d u

= \int \frac{1}{u ^{3}} d u

Apply the Power Rule

: - \frac{1}{2 u ^{2}}

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

Substitute back

u = arcsin (x)

= - \frac{1}{2 arcsin ^{2} ( x )}

Add a constant to the solution

= - \frac{1}{2 arcsin ^{2} ( x )} + C

e^{4 (t - 3)}

x \to 1 - lim (\frac{- 1}{x ^{2} - 1})

\int \frac{1}{1 - 5 x} d x

\frac{d r}{d θ} r = (7 + sec (θ)) sin (θ)

x^{2} 3 x + 5

What is the integral of 1/((arcsin(x))^3sqrt(1-x^2)) ?
The integral of 1/((arcsin(x))^3sqrt(1-x^2)) is -1/(2arcsin^2(x))+C