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

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

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integral of 1/(sqrt(-x^2+4))

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

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

Solution steps

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

Apply Trigonometric Substitution

= \int 1 d u

Integral of a constant:

\int a d x = a x

= 1 \cdot u

Substitute back

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

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

Simplify

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

Add a constant to the solution

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

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