What is the integral of (3r)/(sqrt(1-r^2)) ?

The integral of (3r)/(sqrt(1-r^2)) is -3sqrt(1-r^2)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (3r)/(sqrt(1-r^2))

\int \frac{3 r}{1 - r ^{2}} d r

- 3 1 - r^{2} + C

Solution steps

\int \frac{3 r}{1 - r ^{2}} d r

Take the constant out:

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

= 3 \cdot \int \frac{r}{1 - r ^{2}} d r

Apply u-substitution

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

= 3 \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

= 3 (- \frac{1}{2} \cdot \int \frac{1}{u} d u)

Apply the Power Rule

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

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

Substitute back

u = 1 - r^{2}

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

Simplify

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

= - 3 1 - r^{2}

Add a constant to the solution

= - 3 1 - r^{2} + C

\int cos^{2} (4 x) d x

y = (\frac{x}{3.3} + \frac{3.3}{x}) (x^{2} + 1)

x \to + 2 lim (2 + 3)

\int (1 + 20 w) w d w

\int \frac{x ^{2}}{( 16 - x ^{2} ) ^{\frac{3}{2}}} d x

What is the integral of (3r)/(sqrt(1-r^2)) ?
The integral of (3r)/(sqrt(1-r^2)) is -3sqrt(1-r^2)+C