What is the integral of 1/(sqrt(324-x^2)) ?

The integral of 1/(sqrt(324-x^2)) is arcsin(1/18 x)+C

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integral of 1/(sqrt(324-x^2))

\int \frac{1}{324 - x ^{2}} d x

arcsin (\frac{1}{18} x) + C

Solution steps

\int \frac{1}{324 - 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}{18} x)

= 1 \cdot arcsin (\frac{1}{18} x)

Simplify

= arcsin (\frac{1}{18} x)

Add a constant to the solution

= arcsin (\frac{1}{18} x) + C

\int tan^{8} (7 x) sec^{4} (7 x) d x

f (x) = x^{2} - 1, at x = - 3

\frac{\partial}{\partial x} (3 y x^{2})

\frac{d}{d x} (5 - 8 x)

\frac{\partial}{\partial y} (- \frac{y ^{3}}{3} - 8 x)

What is the integral of 1/(sqrt(324-x^2)) ?
The integral of 1/(sqrt(324-x^2)) is arcsin(1/18 x)+C