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

The integral of 1/(x^2sqrt(2+9x^2)) is -1/(sqrt(11)x)+C

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

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

- \frac{1}{11 x} + C

Solution steps

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

Apply exponent rule:

\frac{1}{a ^{b}} = a^{- b}

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

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

Take the constant out:

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

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

Simplify

= \frac{1}{11} \cdot \int x^{- 2} d x

Apply the Power Rule

: - \frac{1}{x}

= \frac{1}{11} (- \frac{1}{x})

Simplify

\frac{1}{11} (- \frac{1}{x}) : - \frac{1}{11 x}

= - \frac{1}{11 x}

Add a constant to the solution

= - \frac{1}{11 x} + C

\frac{\partial}{\partial y} ((x^{2} + y^{2}) ln (x^{2} + y^{2}))

5 t^{- \frac{3}{5}}

\frac{5}{3 - 2 x}

\int sec^{4} (4 x) d x

x \to - 2 lim (x^{2} + 1)

What is the integral of 1/(x^2sqrt(2+9x^2)) ?
The integral of 1/(x^2sqrt(2+9x^2)) is -1/(sqrt(11)x)+C