What is the integral of ((-7)/x+e^{9x}+9/4) ?

The integral of ((-7)/x+e^{9x}+9/4) is -7ln|x|+1/9 e^{9x}+9/4 x+C

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integral of ((-7)/x+e^{9x}+9/4)

\int (\frac{- 7}{x} + e^{9 x} + \frac{9}{4}) d x

- 7 ln ∣ x ∣ + \frac{1}{9} e^{9 x} + \frac{9}{4} x + C

Solution steps

\int \frac{- 7}{x} + e^{9 x} + \frac{9}{4} 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 \frac{- 7}{x} d x + \int e^{9 x} d x + \int \frac{9}{4} d x

\int \frac{- 7}{x} d x = - 7 ln ∣ x ∣

\int e^{9 x} d x = \frac{1}{9} e^{9 x}

\int \frac{9}{4} d x = \frac{9}{4} x

= - 7 ln ∣ x ∣ + \frac{1}{9} e^{9 x} + \frac{9}{4} x

Add a constant to the solution

= - 7 ln ∣ x ∣ + \frac{1}{9} e^{9 x} + \frac{9}{4} x + C

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What is the integral of ((-7)/x+e^{9x}+9/4) ?
The integral of ((-7)/x+e^{9x}+9/4) is -7ln|x|+1/9 e^{9x}+9/4 x+C