What is the integral of (1/3 e^{x+3}+3/x-5) ?

The integral of (1/3 e^{x+3}+3/x-5) is 1/3 e^{3+x}+3ln|x|-5x+C

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integral of (1/3 e^{x+3}+3/x-5)

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

\frac{1}{3} e^{3 + x} + 3 ln ∣ x ∣ - 5 x + C

Solution steps

\int \frac{1}{3} e^{x + 3} + \frac{3}{x} - 5 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}{3} e^{x + 3} d x + \int \frac{3}{x} d x - \int 5 d x

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

\int \frac{3}{x} d x = 3 ln ∣ x ∣

\int 5 d x = 5 x

= \frac{1}{3} e^{3 + x} + 3 ln ∣ x ∣ - 5 x

Add a constant to the solution

= \frac{1}{3} e^{3 + x} + 3 ln ∣ x ∣ - 5 x + C

\int \frac{x ^{2} - 11 x - 18}{x ( x ^{2} + 3 x + 3 )} d x

\frac{\partial}{\partial x} (5 x y - 4 x^{2} y)

\frac{\partial}{\partial x} (x)

x \to 0 lim (sin^{4} (x))

cos (2 (t - \frac{5 π}{2}))

What is the integral of (1/3 e^{x+3}+3/x-5) ?
The integral of (1/3 e^{x+3}+3/x-5) is 1/3 e^{3+x}+3ln|x|-5x+C