What is the integral of (1/x-6e^x) ?

The integral of (1/x-6e^x) is ln|x|-6e^x+C

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integral of (1/x-6e^x)

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

ln ∣ x ∣ - 6 e^{x} + C

Solution steps

\int \frac{1}{x} - 6 e^{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{1}{x} d x - \int 6 e^{x} d x

\int \frac{1}{x} d x = ln ∣ x ∣

\int 6 e^{x} d x = 6 e^{x}

= ln ∣ x ∣ - 6 e^{x}

Add a constant to the solution

= ln ∣ x ∣ - 6 e^{x} + C

\int \frac{3}{4 + x ^{2}} d x

y d y + (1 + y^{2}) sin (t) d t = 0

\frac{d}{d x} (e x)

\frac{d}{d x} ((3 x - 2)^{2})

y = 1 + x