What is the integral of (8x^3+1/x) ?

The integral of (8x^3+1/x) is 2x^4+ln|x|+C

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integral of (8x^3+1/x)

\int (8 x^{3} + \frac{1}{x}) d x

2 x^{4} + ln ∣ x ∣ + C

Solution steps

\int 8 x^{3} + \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 8 x^{3} d x + \int \frac{1}{x} d x

\int 8 x^{3} d x = 2 x^{4}

\int \frac{1}{x} d x = ln ∣ x ∣

= 2 x^{4} + ln ∣ x ∣

Add a constant to the solution

= 2 x^{4} + ln ∣ x ∣ + C