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

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

Popular >

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

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

2 arcsin (\frac{1}{2} x) + C

Solution steps

\int \frac{2}{4 - 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{1}{4 - x ^{2}} d x

Apply Trigonometric Substitution

: \int 1 d u

= 2 \cdot \int 1 d u

Integral of a constant:

\int a d x = a x

= 2 \cdot 1 \cdot u

Substitute back

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

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

Simplify

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

Add a constant to the solution

= 2 arcsin (\frac{1}{2} x) + C

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

y^{^{'}} (t) = (y + 1) \cdot (y - 3), y (0) = 1

\frac{d}{d x} (lo g_{10} (sin (x)))

x \to - 4 lim (5 x + 20 - 8)

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

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