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

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

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

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

- 2 - x^{2} + C

Solution steps

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

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

Simplify

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

= - 2 - x^{2}

Add a constant to the solution

= - 2 - x^{2} + C

x \to \infty lim (7 x - 3)

\frac{\partial}{\partial x} (\frac{x ^{2}}{x ^{2} + 1})

(\frac{f ( t )}{g ( t )})^{'}

\frac{d}{d x} (x e^{x^{2}} (x^{2} + 1)^{10})

x \frac{d y}{d x} = 2 x^{2} + y, y (1) = 3

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