What is the integral of (12e^x-5x^{-2}) ?

The integral of (12e^x-5x^{-2}) is 12e^x+5/x+C

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integral of (12e^x-5x^{-2})

\int (12 e^{x} - 5 x^{- 2}) d x

12 e^{x} + \frac{5}{x} + C

Solution steps

\int 12 e^{x} - 5 x^{- 2} 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 12 e^{x} d x - \int 5 x^{- 2} d x

\int 12 e^{x} d x = 12 e^{x}

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

= 12 e^{x} - (- \frac{5}{x})

Simplify

= 12 e^{x} + \frac{5}{x}

Add a constant to the solution

= 12 e^{x} + \frac{5}{x} + C

\frac{d}{d x} ((x^{2} - \frac{1}{x ^{2}})^{6})

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\frac{( x + 9 )}{x}

\frac{d}{d t} (\frac{1}{t ^{4}})

What is the integral of (12e^x-5x^{-2}) ?
The integral of (12e^x-5x^{-2}) is 12e^x+5/x+C