What is the integral of (x/6+6/x) ?

The integral of (x/6+6/x) is (x^2)/(12)+6ln|x|+C

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integral of (x/6+6/x)

\int (\frac{x}{6} + \frac{6}{x}) d x

\frac{x ^{2}}{12} + 6 ln ∣ x ∣ + C

Solution steps

\int \frac{x}{6} + \frac{6}{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{x}{6} d x + \int \frac{6}{x} d x

\int \frac{x}{6} d x = \frac{x ^{2}}{12}

\int \frac{6}{x} d x = 6 ln ∣ x ∣

= \frac{x ^{2}}{12} + 6 ln ∣ x ∣

Add a constant to the solution

= \frac{x ^{2}}{12} + 6 ln ∣ x ∣ + C

\int x^{2} x^{2} - 4 d x

\frac{d}{d x} (\frac{8}{5 x ^{4}})

y^{^{''}} + 25 y = csc^{2} (5 t)

(- 1, - 6), (- 15, 2)

x \to 1 lim (∣ x - 4 ∣ + 2)

What is the integral of (x/6+6/x) ?
The integral of (x/6+6/x) is (x^2)/(12)+6ln|x|+C