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 0 lim (18 + \frac{20}{x ^{3}})

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

\int - x sin (z) d z

\int (2 + x + x^{2} + 3 x^{3}) d x

\frac{d}{d x} (\frac{x + 5}{x - 3})

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