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

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

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Integrate Using u-Substitution integral of square root of 4-x^2 with respect to x

substitution

\int (4 - x^{2}) d x

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

Solution steps

\int 4 - x^{2} d x

Apply u-substitution:

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

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

x \to 1 - lim (\frac{( x - 1 )}{( x ^{2} - 4 )})

(- 3, 3), (5, 9)

x \to - \infty lim (\frac{( x ^{4} - 1 )}{( x ^{3} - 1 )})

\int \frac{( ln ( x ) )}{x} d x

\int (\frac{( x ^{2} - 9 )}{( x ^{3} )}) d x

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