What is the integral of-9e^{-9x}+(-7x+5x^5)/(x^2) ?

The integral of-9e^{-9x}+(-7x+5x^5)/(x^2) is e^{-9x}-7ln|x|+(5x^4)/4+C

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integral of-9e^{-9x}+(-7x+5x^5)/(x^2)

\int - 9 e^{- 9 x} + \frac{- 7 x + 5 x ^{5}}{x ^{2}} d x

e^{- 9 x} - 7 ln ∣ x ∣ + \frac{5 x ^{4}}{4} + C

Solution steps

\int - 9 e^{- 9 x} + \frac{- 7 x + 5 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 9 e^{- 9 x} d x + \int \frac{- 7 x + 5 x ^{5}}{x ^{2}} d x

\int 9 e^{- 9 x} d x = - e^{- 9 x}

\int \frac{- 7 x + 5 x ^{5}}{x ^{2}} d x = - 7 ln ∣ x ∣ + \frac{5 x ^{4}}{4}

= - (- e^{- 9 x}) - 7 ln ∣ x ∣ + \frac{5 x ^{4}}{4}

Simplify

= e^{- 9 x} - 7 ln ∣ x ∣ + \frac{5 x ^{4}}{4}

Add a constant to the solution

= e^{- 9 x} - 7 ln ∣ x ∣ + \frac{5 x ^{4}}{4} + C

x \to 2 lim (3 x^{2} + 7 x - 15)

\int (\frac{a}{b x} + \frac{x}{c ^{2} x + x ^{3}}) d x

\frac{d y}{d x} + 3 y = 0

6 - x^{2}

ln (\frac{1}{3}) (2 + e^{- 3 x})

What is the integral of-9e^{-9x}+(-7x+5x^5)/(x^2) ?
The integral of-9e^{-9x}+(-7x+5x^5)/(x^2) is e^{-9x}-7ln|x|+(5x^4)/4+C