What is the integral of x/(sqrt(9x^2-1)) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x/(sqrt(9x^2-1))

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

\frac{1}{9} 9 x^{2} - 1 + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{18 u} d u

= \int \frac{1}{18 u} d u

Take the constant out:

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

= \frac{1}{18} \cdot \int \frac{1}{u} d u

Apply the Power Rule

: 2 u^{\frac{1}{2}}

= \frac{1}{18} \cdot 2 u^{\frac{1}{2}}

Substitute back

u = 9 x^{2} - 1

= \frac{1}{18} \cdot 2 (9 x^{2} - 1)^{\frac{1}{2}}

Simplify

\frac{1}{18} \cdot 2 (9 x^{2} - 1)^{\frac{1}{2}} : \frac{1}{9} 9 x^{2} - 1

= \frac{1}{9} 9 x^{2} - 1

Add a constant to the solution

= \frac{1}{9} 9 x^{2} - 1 + C

\int \frac{1}{x ^{2} + 8 x + 19} d x

\frac{\partial}{\partial x} (ln (y x))

\int sin (r^{2}) r d r

\int \frac{6 ^{x} - 4 \cdot 1 5 ^{x}}{3 ^{2 x}} d x

ln (ln (6 s))

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