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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

Popular Examples

integral of (z+1)e^{8z}

\int (z + 1) e^{8 z} d z

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

\frac{1}{( x + y ) ^{2}}

integral of (2-e)

\int (2 - e) d x

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

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

integral of e^{-((x-3)^2)/2}

\int e^{- \frac{( x - 3 ) ^{2}}{2}} 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