What is the integral of (-3x^{-2.5}-7x^{-1}) ?

The integral of (-3x^{-2.5}-7x^{-1}) is 2/(x^{1.5)}-7ln|x|+C

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integral of (-3x^{-2.5}-7x^{-1})

\int (- 3 x^{- 2.5} - 7 x^{- 1}) d x

\frac{2}{x ^{1.5}} - 7 ln ∣ x ∣ + C

Solution steps

\int - 3 x^{- 2.5} - 7 x^{- 1} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int 3 x^{- 2.5} d x - \int 7 x^{- 1} d x

\int 3 x^{- 2.5} d x = - \frac{2}{x ^{1.5}}

\int 7 x^{- 1} d x = 7 ln ∣ x ∣

= - (- \frac{2}{x ^{1.5}}) - 7 ln ∣ x ∣

Simplify

= \frac{2}{x ^{1.5}} - 7 ln ∣ x ∣

Add a constant to the solution

= \frac{2}{x ^{1.5}} - 7 ln ∣ x ∣ + C

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What is the integral of (-3x^{-2.5}-7x^{-1}) ?
The integral of (-3x^{-2.5}-7x^{-1}) is 2/(x^{1.5)}-7ln|x|+C