What is the integral of 9/(sqrt(81-9x^2)) ?

The integral of 9/(sqrt(81-9x^2)) is 3arcsin(1/3 x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 9/(sqrt(81-9x^2))

\int \frac{9}{81 - 9 x ^{2}} d x

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

Solution steps

\int \frac{9}{81 - 9 x ^{2}} d x

Take the constant out:

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

= 9 \cdot \int \frac{1}{81 - 9 x ^{2}} d x

Apply Trigonometric Substitution

: \int \frac{1}{3} d u

= 9 \cdot \int \frac{1}{3} d u

Take the constant out:

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

= 9 \cdot \frac{1}{3} \cdot \int 1 d u

Integral of a constant:

\int a d x = a x

= 9 \cdot \frac{1}{3} \cdot 1 \cdot u

Substitute back

u = arcsin (\frac{3}{9} x)

= 9 \cdot \frac{1}{3} \cdot 1 \cdot arcsin (\frac{3}{9} x)

Simplify

9 \cdot \frac{1}{3} \cdot 1 \cdot arcsin (\frac{3}{9} x) : 3 arcsin (\frac{1}{3} x)

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

Add a constant to the solution

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

\frac{d}{d x} (6 y cos (x))

x \to 81 lim (lo g_{243} (x))

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

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

4 x^{2}, at x = 3

What is the integral of 9/(sqrt(81-9x^2)) ?
The integral of 9/(sqrt(81-9x^2)) is 3arcsin(1/3 x)+C