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

The integral of (x+3)/(sqrt(4-x^2)) is -sqrt(4-x^2)+3arcsin(1/2 x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

- 4 - x^{2} + 3 arcsin (\frac{1}{2} x) + C

Solution steps

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

Apply Trigonometric Substitution

: \int 2 sin (u) + 3 d u

= \int 2 sin (u) + 3 d u

Apply the Sum Rule:

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

= \int 2 sin (u) d u + \int 3 d u

\int 2 sin (u) d u = - 2 cos (u)

\int 3 d u = 3 u

= - 2 cos (u) + 3 u

Substitute back

u = arcsin (\frac{1}{2} x)

= - 2 cos (arcsin (\frac{1}{2} x)) + 3 arcsin (\frac{1}{2} x)

Simplify

- 2 cos (arcsin (\frac{1}{2} x)) + 3 arcsin (\frac{1}{2} x) : - 4 - x^{2} + 3 arcsin (\frac{1}{2} x)

= - 4 - x^{2} + 3 arcsin (\frac{1}{2} x)

Add a constant to the solution

= - 4 - x^{2} + 3 arcsin (\frac{1}{2} x) + C

2 x + 1, at x = \frac{1}{4}

n = 1 \sum \infty e^{- n} n!

f (x) = 8^{x}

x \to 8 - lim (\frac{2}{x - 8})

y^{^{''}} + 25 y = sec (5 t)

What is the integral of (x+3)/(sqrt(4-x^2)) ?
The integral of (x+3)/(sqrt(4-x^2)) is -sqrt(4-x^2)+3arcsin(1/2 x)+C