What is the integral of e^{3x}+1/x ?

The integral of e^{3x}+1/x is 1/3 e^{3x}+ln|x|+C

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integral of e^{3x}+1/x

\int e^{3 x} + \frac{1}{x} d x

\frac{1}{3} e^{3 x} + ln ∣ x ∣ + C

Solution steps

\int e^{3 x} + \frac{1}{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 e^{3 x} d x + \int \frac{1}{x} d x

\int e^{3 x} d x = \frac{1}{3} e^{3 x}

\int \frac{1}{x} d x = ln ∣ x ∣

= \frac{1}{3} e^{3 x} + ln ∣ x ∣

Add a constant to the solution

= \frac{1}{3} e^{3 x} + ln ∣ x ∣ + C

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

y^{^{'}} + 3 y = 2 e^{- 3 t}

f (x) = \frac{( x - 2 )}{( 2 x ^{2} + 3 )}

\int_{2}^{3} \frac{1}{x ^{2} - 4 x} d x

What is the integral of e^{3x}+1/x ?
The integral of e^{3x}+1/x is 1/3 e^{3x}+ln|x|+C