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

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

Popular >

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

\int x \frac{1}{1 - x ^{2}} d x

- 1 - x^{2} + C

Solution steps

\int x \frac{1}{1 - x ^{2}} d x

Apply u-substitution

: \int - \frac{1}{2 u} d u

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

Take the constant out:

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

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

Apply the Power Rule

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

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

Substitute back

u = 1 - x^{2}

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

Simplify

- \frac{1}{2} \cdot 2 (1 - x^{2})^{\frac{1}{2}} : - 1 - x^{2}

= - 1 - x^{2}

Add a constant to the solution

= - 1 - x^{2} + C

\frac{d}{d x} (10 cos^{3} (x))

f (x) = sin (x) + \frac{3}{4} cot (x)

\frac{1}{x ^{- 9}}

\frac{d}{d x} ((1 + \frac{7}{x})^{5})

y = ln (x^{2} - 9)

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