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} (x, (x))

x \to - 2 lim (x^{2} - a)

\frac{d y}{d x} = x^{10 c o s (x)}

\int \frac{t}{t ^{4} + 9} d t

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