What is the integral of (5e^{2x}+1/x) ?

The integral of (5e^{2x}+1/x) is 5/2 e^{2x}+ln|x|+C

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integral of (5e^{2x}+1/x)

\int (5 e^{2 x} + \frac{1}{x}) d x

\frac{5}{2} e^{2 x} + ln ∣ x ∣ + C

Solution steps

\int 5 e^{2 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 5 e^{2 x} d x + \int \frac{1}{x} d x

\int 5 e^{2 x} d x = \frac{5}{2} e^{2 x}

\int \frac{1}{x} d x = ln ∣ x ∣

= \frac{5}{2} e^{2 x} + ln ∣ x ∣

Add a constant to the solution

= \frac{5}{2} e^{2 x} + ln ∣ x ∣ + C

\frac{d}{d x} (sin (k t))

f (x) = (5 + 2 x) e^{- 3 x}

\frac{d}{d x} (2 \cdot e^{2 x})

\int_{3}^{4} \frac{1}{sin ( x )} d x

5 cos (2 t) - 3 sin (3 t)

What is the integral of (5e^{2x}+1/x) ?
The integral of (5e^{2x}+1/x) is 5/2 e^{2x}+ln|x|+C