What is the integral of 1/(b^2x^2sqrt(a^2-cx^2)) ?

The integral of 1/(b^2x^2sqrt(a^2-cx^2)) is -1/(b^2xsqrt(a^2-c))+C

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integral of 1/(b^2x^2sqrt(a^2-cx^2))

\int \frac{1}{b ^{2} x ^{2} a ^{2} - c x ^{2}} d x

- \frac{1}{b ^{2} x a ^{2} - c} + C

Solution steps

\int \frac{1}{b ^{2} x ^{2} a ^{2} - c x ^{2}} d x

Take the constant out:

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

= \frac{1}{b ^{2}} \cdot \int \frac{1}{x ^{2} a ^{2} - c x ^{2}} d x

Apply exponent rule:

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

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

= \frac{1}{b ^{2}} \cdot \int x^{- 2} \frac{1}{a ^{2} - c} d x

Take the constant out:

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

= \frac{1}{b ^{2}} \cdot \frac{1}{a ^{2} - c} \cdot \int x^{- 2} d x

Apply the Power Rule

: - \frac{1}{x}

= \frac{1}{b ^{2}} \cdot \frac{1}{a ^{2} - c} (- \frac{1}{x})

Simplify

\frac{1}{b ^{2}} \cdot \frac{1}{a ^{2} - c} (- \frac{1}{x}) : - \frac{1}{b ^{2} x a ^{2} - c}

= - \frac{1}{b ^{2} x a ^{2} - c}

Add a constant to the solution

= - \frac{1}{b ^{2} x a ^{2} - c} + C

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What is the integral of 1/(b^2x^2sqrt(a^2-cx^2)) ?
The integral of 1/(b^2x^2sqrt(a^2-cx^2)) is -1/(b^2xsqrt(a^2-c))+C