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

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

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

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

\frac{x}{1 - x ^{2}} + C

Solution steps

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

(1 - x^{2})^{3} = (1 - x^{2})^{\frac{3}{2}},

assuming

(1 - x^{2}) \geq 0

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

Apply Trigonometric Substitution

: \int sec^{2} (u) d u

= \int sec^{2} (u) d u

Use the common integral:

\int sec^{2} (u) d u = tan (u)

= tan (u)

Substitute back

u = arcsin (x)

= tan (arcsin (x))

Use the following identity:

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

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

Add a constant to the solution

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

\frac{d}{d x} (\frac{ln ( x )}{9 x})

\int (\frac{1}{e ^{3 t}}) d t

x \to 0 lim (\frac{e - 1}{x})

\frac{d}{d x} (x^{4} - 3 x^{2} + 3)

x \to 1 lim (\frac{∣ 3 - x ∣}{3 - x})

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