What is the integral of 5/x+12x^5 ?

The integral of 5/x+12x^5 is 5ln|x|+2x^6+C

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integral of 5/x+12x^5

\int \frac{5}{x} + 12 x^{5} d x

5 ln ∣ x ∣ + 2 x^{6} + C

Solution steps

\int \frac{5}{x} + 12 x^{5} 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 12 x^{5} d x

\int \frac{5}{x} d x = 5 ln ∣ x ∣

\int 12 x^{5} d x = 2 x^{6}

= 5 ln ∣ x ∣ + 2 x^{6}

Add a constant to the solution

= 5 ln ∣ x ∣ + 2 x^{6} + C

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