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 4^{7 x} d x

x \to - 1 lim (x + 5 - 2)

5^{x^{4}}

3 x^{2} y + x^{3} y^{^{'}} = - 7 sec^{2} (x) tan (x)

f (x) = 2 x^{3} - 4 x + 6

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