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

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

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

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

1 - x^{2} + C

Solution steps

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

Take the constant out:

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

= - \int \frac{x}{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} (c x e^{- 2 x})

\frac{d}{d x} (\frac{2 sin ( x )}{x})

x \to 2 lim (\frac{x ^{2} - 4}{x ^{2} - 3 - 1})

\frac{\partial}{\partial z} (y z^{2})

\frac{\partial}{\partial x} (ln (x \cdot y))

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