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Popular >

integral of+5e^x-1/x

Solution

\int + 5 e^{x} - \frac{1}{x} d x

Solution

5 e^{x} - ln ∣ x ∣ + C

Solution steps

\int 5 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 5 e^{x} d x - \int \frac{1}{x} d x

\int 5 e^{x} d x = 5 e^{x}

\int \frac{1}{x} d x = ln ∣ x ∣

= 5 e^{x} - ln ∣ x ∣

Add a constant to the solution

= 5 e^{x} - ln ∣ x ∣ + C

Popular Examples

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\int (sec^{2} (x) \cdot tan (x)) d x

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\int \frac{1}{y ^{2} + 10 y + 30} d y

integral of x^1(2+2x^2)^3

\int x^{1} (2 + 2 x^{2})^{3} d x

integral of 1/(x^3)*sin(1/(x^2))

\int \frac{1}{x ^{3}} \cdot sin (\frac{1}{x ^{2}}) d x

integral of (x+5)/(\sqrt[5]{x-5)}

Frequently Asked Questions (FAQ)

What is the integral of+5e^x-1/x ?
The integral of+5e^x-1/x is 5e^x-ln|x|+C