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Popular >

integral of (1/x-e^x)

Solution

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

Solution

ln ∣ x ∣ - e^{x} + C

Solution steps

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

\int \frac{1}{x} d x = ln ∣ x ∣

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

= ln ∣ x ∣ - e^{x}

Add a constant to the solution

= ln ∣ x ∣ - e^{x} + C

Graph

Popular Examples

integral of cos^2(2x)sin(7x)

\int cos^{2} (2 x) sin (7 x) d x

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

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

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

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

integral of e^{3x+6}

\int e^{3 x + 6} d x

integral of (4x-3)(x-3)

\int (4 x - 3) (x - 3) d x

Frequently Asked Questions (FAQ)

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