What is the integral of (-x)/(sqrt(4-x^2)) ?

The integral of (-x)/(sqrt(4-x^2)) is sqrt(4-x^2)+C

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integral of (-x)/(sqrt(4-x^2))

\int \frac{- x}{4 - x ^{2}} d x

4 - x^{2} + C

Solution steps

\int \frac{- x}{4 - 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}{4 - 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 = 4 - x^{2}

= - (- \frac{1}{2} \cdot 2 (4 - x^{2})^{\frac{1}{2}})

Simplify

- (- \frac{1}{2} \cdot 2 (4 - x^{2})^{\frac{1}{2}}) : 4 - x^{2}

= 4 - x^{2}

Add a constant to the solution

= 4 - x^{2} + C

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

x^{2} + y^{2} = 25, (- 3, 4)

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

\int x sec^{2} (x) d x

\int \frac{sec ^{2} ( 3 ) t}{t} d t

What is the integral of (-x)/(sqrt(4-x^2)) ?
The integral of (-x)/(sqrt(4-x^2)) is sqrt(4-x^2)+C