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

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

\int_{0}^{\infty} x^{- 3} d x

\frac{d}{d z} (9 x^{\frac{y}{z}})

\int (2 x + 1) e^{x^{2} + 1} d x

\frac{1}{( x - 2 )}

\frac{d ^{2} y}{d t ^{2}} + 3 \frac{d y}{d t} - 40 y = 1 - 4 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