What is the integral of (5x)/(sqrt(4-x^2)) ?

The integral of (5x)/(sqrt(4-x^2)) is -5sqrt(4-x^2)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (5x)/(sqrt(4-x^2))

\int \frac{5 x}{4 - x ^{2}} d x

- 5 4 - x^{2} + C

Solution steps

\int \frac{5 x}{4 - x ^{2}} d x

Take the constant out:

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

= 5 \cdot \int \frac{x}{4 - x ^{2}} d x

Apply u-substitution

= 5 \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

= 5 (- \frac{1}{2} \cdot \int \frac{1}{u} d u)

Apply the Power Rule

= 5 (- \frac{1}{2} \cdot 2 u^{\frac{1}{2}})

Substitute back

u = 4 - x^{2}

= 5 (- \frac{1}{2} \cdot 2 (4 - x^{2})^{\frac{1}{2}})

Simplify

5 (- \frac{1}{2} \cdot 2 (4 - x^{2})^{\frac{1}{2}}) : - 5 4 - x^{2}

= - 5 4 - x^{2}

Add a constant to the solution

= - 5 4 - x^{2} + C

What is the integral of (5x)/(sqrt(4-x^2)) ?
The integral of (5x)/(sqrt(4-x^2)) is -5sqrt(4-x^2)+C