What is the integral of (-2e^{3x}+5/x) ?

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

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integral of (-2e^{3x}+5/x)

\int (- 2 e^{3 x} + \frac{5}{x}) d x

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

Solution steps

\int - 2 e^{3 x} + \frac{5}{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^{3 x} d x + \int \frac{5}{x} d x

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

\int \frac{5}{x} d x = 5 ln ∣ x ∣

= - \frac{2}{3} e^{3 x} + 5 ln ∣ x ∣

Add a constant to the solution

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

x \to + 1 lim (ln (x))

\int \frac{4 x ^{3} - 5 x ^{2}}{( x - 2 ) ( x + 1 )} d x

6 x, \frac{2}{3} x, 40 - x^{2}

\frac{d}{d x} (6 cos (x) sin (x))

\frac{\partial}{\partial x} (e^{5 y})

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