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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

Popular Examples

f(x)=sin(cos(x))

f (x) = sin (cos (x))

integral of 3/(x^2+2)

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

integral of 18sec^4(x)

\int 18 sec^{4} (x) d x

limit as h approaches 0 of sin(1/h)

h \to 0 lim (sin (\frac{1}{h}))

integral of 2sin^3(2x)cos^3(2x)

\int 2 sin^{3} (2 x) cos^{3} (2 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