What is the integral of (2x)/(sqrt(3-x^2)) ?

The integral of (2x)/(sqrt(3-x^2)) is -2sqrt(3-x^2)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (2x)/(sqrt(3-x^2))

\int \frac{2 x}{3 - x ^{2}} d x

- 2 3 - x^{2} + C

Solution steps

\int \frac{2 x}{3 - x ^{2}} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int \frac{x}{3 - x ^{2}} d x

Apply u-substitution

: \int - \frac{1}{2 u} d u

= 2 \cdot \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

= 2 (- \frac{1}{2} \cdot \int \frac{1}{u} d u)

Apply the Power Rule

: 2 u^{\frac{1}{2}}

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

Substitute back

u = 3 - x^{2}

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

Simplify

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

= - 2 3 - x^{2}

Add a constant to the solution

= - 2 3 - x^{2} + C

\int \frac{4}{x ln ( x ^{4} )} d x

\int cos (t) sin^{5} (t) d t

\int \frac{π x}{12} d x

\int 2 t - 6 d t

What is the integral of (2x)/(sqrt(3-x^2)) ?
The integral of (2x)/(sqrt(3-x^2)) is -2sqrt(3-x^2)+C