What is the integral of 1/(sqrt(12-x^2)) ?

The integral of 1/(sqrt(12-x^2)) is arcsin(1/(2sqrt(3))x)+C

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integral of 1/(sqrt(12-x^2))

\int \frac{1}{12 - x ^{2}} d x

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

Solution steps

\int \frac{1}{12 - 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 3} x)

= 1 \cdot arcsin (\frac{1}{2 3} x)

Simplify

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

Add a constant to the solution

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

\frac{d}{d x} (3 x^{2} - 6 x)

y = sin (π x)

x \to - 1 lim (\frac{3 x - 7}{2 x + 5})

x \to - \infty lim (\frac{2}{x} + 1)

x \to 0 lim (1 + x^{3})

What is the integral of 1/(sqrt(12-x^2)) ?
The integral of 1/(sqrt(12-x^2)) is arcsin(1/(2sqrt(3))x)+C