What is the integral of x/(sqrt(12-9x^2)) ?

The integral of x/(sqrt(12-9x^2)) is -1/9 sqrt(12-9x^2)+C

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integral of x/(sqrt(12-9x^2))

\int \frac{x}{12 - 9 x ^{2}} d x

- \frac{1}{9} 12 - 9 x^{2} + C

Solution steps

\int \frac{x}{12 - 9 x ^{2}} 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 = 12 - 9 x^{2}

= - \frac{1}{18} \cdot 2 (12 - 9 x^{2})^{\frac{1}{2}}

Simplify

- \frac{1}{18} \cdot 2 (12 - 9 x^{2})^{\frac{1}{2}} : - \frac{1}{9} 12 - 9 x^{2}

= - \frac{1}{9} 12 - 9 x^{2}

Add a constant to the solution

= - \frac{1}{9} 12 - 9 x^{2} + C

\int_{1}^{4} x (2 + x) d x

w \to 0 lim (\frac{w ^{2}}{cos ( w ) - 1})

2 n d e^{2 e^{x}}

n = 1 \sum \infty \frac{n ^{2}}{3}

(3) (6.9)

What is the integral of x/(sqrt(12-9x^2)) ?
The integral of x/(sqrt(12-9x^2)) is -1/9 sqrt(12-9x^2)+C