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Popular >

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

Popular Examples

integral of 1/(sqrt(3-3x^2))

\int \frac{1}{3 - 3 x ^{2}} d x

integral of (2x)/((x-3)^5)

\int \frac{2 x}{( x - 3 ) ^{5}} d x

integral of xsin(x)e^x

\int x sin (x) e^{x} d x

integral of sec^4(x)tan^5(x)

\int sec^{4} (x) tan^{5} (x) d x

integral of xy^4

\int x y^{4} 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