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

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

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

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

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

Solution steps

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

Simplify

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

Apply Trigonometric Substitution

: \int 1 d u

= \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

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\int cot (25 x) d x

\int x sinh (2 - x^{2}) d x

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

\int \frac{1 + e ^{x}}{x + e ^{x}} d x

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