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Popular >

integral of e/x+x/e

Solution

\int \frac{e}{x} + \frac{x}{e} d x

Solution

e ln ∣ x ∣ + \frac{x ^{2}}{2 e} + C

Solution steps

\int \frac{e}{x} + \frac{x}{e} 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{e}{x} d x + \int \frac{x}{e} d x

\int \frac{e}{x} d x = e ln ∣ x ∣

\int \frac{x}{e} d x = \frac{x ^{2}}{2 e}

= e ln ∣ x ∣ + \frac{x ^{2}}{2 e}

Add a constant to the solution

= e ln ∣ x ∣ + \frac{x ^{2}}{2 e} + C

Popular Examples

integral of sec^2(x)cos(x)

\int sec^{2} (x) cos (x) d x

area y=x^2-1,y=x+1 area

y = x^{2} - 1, y = x + 1

derivative of ln(x^4+27)

\frac{d}{d x} (ln (x^{4} + 27))

integral of 1/(9x^3)

\int \frac{1}{9 x ^{3}} d x

integral from 1.5 to 2 of (2x)/3

\int_{1.5}^{2} \frac{2 x}{3} d x

Frequently Asked Questions (FAQ)

What is the integral of e/x+x/e ?
The integral of e/x+x/e is eln|x|+(x^2)/(2e)+C