What is the integral of ((-6x^6-4x)/(x^2)-4e^{6x}) ?

The integral of ((-6x^6-4x)/(x^2)-4e^{6x}) is -(6x^5)/5-4ln|x|-2/3 e^{6x}+C

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integral of ((-6x^6-4x)/(x^2)-4e^{6x})

\int (\frac{- 6 x ^{6} - 4 x}{x ^{2}} - 4 e^{6 x}) d x

- \frac{6 x ^{5}}{5} - 4 ln ∣ x ∣ - \frac{2}{3} e^{6 x} + C

Solution steps

\int \frac{- 6 x ^{6} - 4 x}{x ^{2}} - 4 e^{6 x} 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{- 6 x ^{6} - 4 x}{x ^{2}} d x - \int 4 e^{6 x} d x

\int \frac{- 6 x ^{6} - 4 x}{x ^{2}} d x = - \frac{6 x ^{5}}{5} - 4 ln ∣ x ∣

\int 4 e^{6 x} d x = \frac{2}{3} e^{6 x}

= - \frac{6 x ^{5}}{5} - 4 ln ∣ x ∣ - \frac{2}{3} e^{6 x}

Add a constant to the solution

= - \frac{6 x ^{5}}{5} - 4 ln ∣ x ∣ - \frac{2}{3} e^{6 x} + C

What is the integral of ((-6x^6-4x)/(x^2)-4e^{6x}) ?
The integral of ((-6x^6-4x)/(x^2)-4e^{6x}) is -(6x^5)/5-4ln|x|-2/3 e^{6x}+C