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Popular Calculus >

integral of (x-5/x)

Solution

\int (x - \frac{5}{x}) d x

Solution

\frac{x ^{2}}{2} - 5 ln ∣ x ∣ + C

Solution steps

\int x - \frac{5}{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 x d x - \int \frac{5}{x} d x

\int x d x = \frac{x ^{2}}{2}

\int \frac{5}{x} d x = 5 ln ∣ x ∣

= \frac{x ^{2}}{2} - 5 ln ∣ x ∣

Add a constant to the solution

= \frac{x ^{2}}{2} - 5 ln ∣ x ∣ + C

Graph

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integral of (x^{11})/(sqrt(2x^6+2))

\int \frac{x ^{11}}{2 x ^{6} + 2} d x

Frequently Asked Questions (FAQ)

What is the integral of (x-5/x) ?
The integral of (x-5/x) is (x^2)/2-5ln|x|+C