What is the integral of e^x-x^e+5/x ?

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

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integral of e^x-x^e+5/x

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

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

Solution steps

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

\int e^{x} d x = e^{x}

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

\int \frac{5}{x} d x = 5 ln ∣ x ∣

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

Add a constant to the solution

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

\int cos (x) cos^{5} (sin (x)) d x

\int \frac{e ^{10 + 3 x}}{5} d x

x \to - 4 lim (- 4)

f (x) = 3 - 8 x^{2}, (- 3, - 69)

\frac{d}{d x} (arctan (3 x^{3}))

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