What is the integral of (5-3x)/(sqrt(4-3x^2)) ?

The integral of (5-3x)/(sqrt(4-3x^2)) is 5/(sqrt(3))arcsin((sqrt(3))/2 x)+sqrt(4-3x^2)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (5-3x)/(sqrt(4-3x^2))

\int \frac{5 - 3 x}{4 - 3 x ^{2}} d x

\frac{5}{3} arcsin (\frac{3}{2} x) + 4 - 3 x^{2} + C

Solution steps

\int \frac{5 - 3 x}{4 - 3 x ^{2}} d x

Expand

\frac{5 - 3 x}{4 - 3 x ^{2}} : \frac{5}{4 - 3 x ^{2}} - \frac{3 x}{4 - 3 x ^{2}}

= \int \frac{5}{4 - 3 x ^{2}} - \frac{3 x}{4 - 3 x ^{2}} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{5}{4 - 3 x ^{2}} d x - \int \frac{3 x}{4 - 3 x ^{2}} d x

\int \frac{5}{4 - 3 x ^{2}} d x = \frac{5}{3} arcsin (\frac{3}{2} x)

\int \frac{3 x}{4 - 3 x ^{2}} d x = - 4 - 3 x^{2}

= \frac{5}{3} arcsin (\frac{3}{2} x) - (- 4 - 3 x^{2})

Simplify

= \frac{5}{3} arcsin (\frac{3}{2} x) + 4 - 3 x^{2}

Add a constant to the solution

= \frac{5}{3} arcsin (\frac{3}{2} x) + 4 - 3 x^{2} + C

\int 2 x e^{5 x^{2}} d x

\int sinh (4 x) cosh (4 x) d x

\int \frac{1}{1 + x ^{2}} + tan^{2} (x) d x

\int 5 e^{- 2 x + 1} d x

\int (x sin^{2} (x)) d x

What is the integral of (5-3x)/(sqrt(4-3x^2)) ?
The integral of (5-3x)/(sqrt(4-3x^2)) is 5/(sqrt(3))arcsin((sqrt(3))/2 x)+sqrt(4-3x^2)+C