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

The integral of (-2e^x-6/x) is -2e^x-6ln|x|+C

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integral of (-2e^x-6/x)

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

- 2 e^{x} - 6 ln ∣ x ∣ + C

Solution steps

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

\int 2 e^{x} d x = 2 e^{x}

\int \frac{6}{x} d x = 6 ln ∣ x ∣

= - 2 e^{x} - 6 ln ∣ x ∣

Add a constant to the solution

= - 2 e^{x} - 6 ln ∣ x ∣ + C

y = \frac{3}{x ^{6}} + \frac{1}{x ^{5}} - \frac{7}{x ^{2}}

\frac{\partial}{\partial x} (x \cdot sin (4 \cdot y \cdot z^{4}))

x \to 0 + lim ((7 x)^{x})

f (x) = 2 x^{2} - 4 x, at x = - 1

f (x) = 4 x - x^{2}, (2, 5)

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