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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

Graph

Popular Examples

integral of (2x-3)^{100}

\int (2 x - 3)^{100} d x

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

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

integral of 4/(3+x^2)

\int \frac{4}{3 + x ^{2}} d x

integral of (3x^2-4x+1)/(x^3-2x^2+x-2)

\int \frac{3 x ^{2} - 4 x + 1}{x ^{3} - 2 x ^{2} + x - 2} d x

integral of (x-1)sin(nx)

\int (x - 1) sin (n x) 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