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

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

Popular >

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

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

- 1 - x^{2} + C

Solution steps

\int \frac{1}{1 - x ^{2}} x 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 e^{\frac{y}{x}})

\frac{\partial}{\partial x} (x + y + ∣ x ∣^{3} y^{2})

\frac{d}{d x} (5 x^{2 π})

(\frac{10 - ( 2 )}{( x )}) \cdot (\frac{3 + ( 1 )}{( x )})

(\frac{1}{1 + e ^{x}})^{^{'}}

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