What is the integral of 7/(x^2sqrt(9a^2-x^2)) ?

The integral of 7/(x^2sqrt(9a^2-x^2)) is -7/(3ax)+C

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integral of 7/(x^2sqrt(9a^2-x^2))

\int \frac{7}{x ^{2} 9 a ^{2} - x ^{2}} d x

- \frac{7}{3 a x} + C

Solution steps

\int \frac{7}{x ^{2} 9 a ^{2} - x ^{2}} d x

Take the constant out:

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

= 7 \cdot \int \frac{1}{x ^{2} 9 a ^{2} - x ^{2}} d x

Apply exponent rule:

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

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

= 7 \cdot \int x^{- 2} \frac{1}{9 a ^{2}} d x

Take the constant out:

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

= 7 \cdot \frac{1}{9 a ^{2}} \cdot \int x^{- 2} d x

9 a^{2} = 3 a^{2}

= 7 \cdot \frac{1}{3 a ^{2}} \cdot \int x^{- 2} d x

Apply the Power Rule

: - \frac{1}{x}

= 7 \cdot \frac{1}{3 a ^{2}} (- \frac{1}{x})

Simplify

7 \cdot \frac{1}{3 a ^{2}} (- \frac{1}{x}) : - \frac{7}{3 a x}

= - \frac{7}{3 a x}

Add a constant to the solution

= - \frac{7}{3 a x} + C

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What is the integral of 7/(x^2sqrt(9a^2-x^2)) ?
The integral of 7/(x^2sqrt(9a^2-x^2)) is -7/(3ax)+C