What is the integral of (-10)/(x^2(25-x^2)^{1/2)} ?

The integral of (-10)/(x^2(25-x^2)^{1/2)} is 2/x+C

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integral of (-10)/(x^2(25-x^2)^{1/2)}

\int \frac{- 10}{x ^{2} ( 25 - x ^{2} ) ^{\frac{1}{2}}} d x

\frac{2}{x} + C

Solution steps

\int \frac{- 10}{x ^{2} ( 25 - x ^{2} ) ^{\frac{1}{2}}} d x

Take the constant out:

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

= - 10 \cdot \int \frac{1}{x ^{2} ( 25 - x ^{2} ) ^{\frac{1}{2}}} d x

Apply exponent rule:

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

\frac{1}{x ^{2} ( 25 - x ^{2} ) ^{\frac{1}{2}}} = x^{- 2} \frac{1}{( 25 - ) ^{\frac{1}{2}}}

= - 10 \cdot \int x^{- 2} \frac{1}{2 5 ^{\frac{1}{2}}} d x

Take the constant out:

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

= - 10 \cdot \frac{1}{2 5 ^{\frac{1}{2}}} \cdot \int x^{- 2} d x

2 5^{\frac{1}{2}} = 5

= - 10 \cdot \frac{1}{5} \cdot \int x^{- 2} d x

Apply the Power Rule

= - 10 \cdot \frac{1}{5} (- \frac{1}{x})

Simplify

- 10 \cdot \frac{1}{5} (- \frac{1}{x}) : \frac{2}{x}

= \frac{2}{x}

Add a constant to the solution

= \frac{2}{x} + C

What is the integral of (-10)/(x^2(25-x^2)^{1/2)} ?
The integral of (-10)/(x^2(25-x^2)^{1/2)} is 2/x+C