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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

y^{''}+64y=7tan(8x)

y^{^{''}} + 64 y = 7 tan (8 x)

limit as x approaches 0 of (x^5+9x)/x

x \to 0 lim (\frac{x ^{5} + 9 x}{x})

derivative of e^{1+x^2}+3x^4 derivative of

e^{1 + x^{2}} + 3 x^{4}

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

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

(dy)/(dx)=x^3-2y

\frac{d y}{d x} = x^{3} - 2 y

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