What is the integral of 16x^3+1/x ?

The integral of 16x^3+1/x is 4x^4+ln|x|+C

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integral of 16x^3+1/x

\int 16 x^{3} + \frac{1}{x} d x

4 x^{4} + ln ∣ x ∣ + C

Solution steps

\int 16 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 16 x^{3} d x + \int \frac{1}{x} d x

\int 16 x^{3} d x = 4 x^{4}

\int \frac{1}{x} d x = ln ∣ x ∣

= 4 x^{4} + ln ∣ x ∣

Add a constant to the solution

= 4 x^{4} + ln ∣ x ∣ + C

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