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

y^{^{'}} = \frac{y ^{2}}{x y + y ^{2}}

\frac{2 t}{2 + t}

t (\frac{d y}{d t}) + 34 y = \frac{1}{t}

y = 3^{c o s (x)}

\int \frac{x ^{3}}{x ^{4} + 9} d x

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