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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 x/((x-1)^2(x^2+1))

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

integral of x^4+x^3-6x^2

\int x^{4} + x^{3} - 6 x^{2} d x

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

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

integral of 4/(sqrt(-u^2+9))

\int \frac{4}{- u ^{2} + 9} d u

integral of (x)^{-1}

\int (x)^{- 1} 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