What is the integral of ((12)/x+x/(12)) ?

The integral of ((12)/x+x/(12)) is 12ln|x|+(x^2)/(24)+C

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integral of ((12)/x+x/(12))

\int (\frac{12}{x} + \frac{x}{12}) d x

12 ln ∣ x ∣ + \frac{x ^{2}}{24} + C

Solution steps

\int \frac{12}{x} + \frac{x}{12} 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{12}{x} d x + \int \frac{x}{12} d x

\int \frac{12}{x} d x = 12 ln ∣ x ∣

\int \frac{x}{12} d x = \frac{x ^{2}}{24}

= 12 ln ∣ x ∣ + \frac{x ^{2}}{24}

Add a constant to the solution

= 12 ln ∣ x ∣ + \frac{x ^{2}}{24} + C

x y^{^{'}} + 3 y = \frac{2 e ^{4 x}}{x ^{2}}

\frac{d}{d x} (a x^{2} e^{- x})

\frac{d}{d x} (ln (\frac{3}{x ^{2} + 9}))

f (x) = x^{x}, at x = 2

(x y^{2} - x) d x + (x^{2} y + y) d y = 0

What is the integral of ((12)/x+x/(12)) ?
The integral of ((12)/x+x/(12)) is 12ln|x|+(x^2)/(24)+C