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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 (3+7x^2)^9*5x

\int (3 + 7 x^{2})^{9} \cdot 5 x d x

integral of (sin^3(x))/(sin^4(x))

\int \frac{sin ^{3} ( x )}{sin ^{4} ( x )} d x

integral of (x^2+60)/(x^2+64)

\int \frac{x ^{2} + 60}{x ^{2} + 64} d x

integral of (2x+1)/(sqrt(x^2+x+1))

\int \frac{2 x + 1}{x ^{2} + x + 1} d x

integral of 5e^{-sqrt(x)}

\int 5 e^{- 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