What is the integral of sqrt(9/(9-x^2)) ?

The integral of sqrt(9/(9-x^2)) is 3arcsin(1/3 x)+C

Popular >

integral of sqrt(9/(9-x^2))

\int \frac{9}{9 - x ^{2}} d x

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

Solution steps

\int \frac{9}{9 - x ^{2}} d x

Simplify

\frac{9}{9 - x ^{2}} : \frac{3}{9 - x ^{2}}

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int \frac{1}{9 - x ^{2}} d x

Apply Trigonometric Substitution

: \int 1 d u

= 3 \cdot \int 1 d u

Integral of a constant:

\int a d x = a x

= 3 \cdot 1 \cdot u

Substitute back

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

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

Simplify

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

Add a constant to the solution

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

\frac{\partial}{\partial x} (ln (\frac{x}{4} + \frac{y}{12}))

\int (e^{- x} sin (x)) d x

\int \frac{x ^{3} + 3 x ^{2}}{x ^{2} + 1} d x

(x^{2} + 1) \cdot \frac{d y}{d x} + 3 x y = 6 x

y = (1 + x) cos (x), at x = 0

What is the integral of sqrt(9/(9-x^2)) ?
The integral of sqrt(9/(9-x^2)) is 3arcsin(1/3 x)+C