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Popular Calculus >

integral of (e^x+1/x)

Solution

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

Solution

e^{x} + ln ∣ x ∣ + C

Solution steps

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

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

\int \frac{1}{x} d x = ln ∣ x ∣

= e^{x} + ln ∣ x ∣

Add a constant to the solution

= e^{x} + ln ∣ x ∣ + C

Graph

Popular Examples

integral of xy^4

\int x y^{4} d x

integral of (x^4+8sqrt(x))/(x^2)

\int \frac{x ^{4} + 8 x}{x ^{2}} d x

integral of 4t^2e^t

\int 4 t^{2} e^{t} d t

integral of 1/((sqrt(x)+\sqrt[4]{x))}

\int \frac{1}{( x + 4 x )} d x

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

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

Frequently Asked Questions (FAQ)

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