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Popular >

integral of 5/x+e^x

Solution

\int \frac{5}{x} + e^{x} d x

Solution

5 ln ∣ x ∣ + e^{x} + C

Solution steps

\int \frac{5}{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{5}{x} d x + \int e^{x} d x

\int \frac{5}{x} d x = 5 ln ∣ x ∣

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

= 5 ln ∣ x ∣ + e^{x}

Add a constant to the solution

= 5 ln ∣ x ∣ + e^{x} + C

Popular Examples

tangent of y=5+5x^2-2x^3 tangent of

y = 5 + 5 x^{2} - 2 x^{3}

integral of (x-5)^2e^x

\int (x - 5)^{2} e^{x} d x

limit as x approaches 8+of 1/((x-8)^2)

x \to 8 + lim (\frac{1}{( x - 8 ) ^{2}})

y^{^{'}} + 3 y = 3

derivative of 5x+3sqrt(x)derivative of

5 x + 3 x

Frequently Asked Questions (FAQ)

What is the integral of 5/x+e^x ?
The integral of 5/x+e^x is 5ln|x|+e^x+C