What is the integral of (29-51x^3)/x ?

The integral of (29-51x^3)/x is 29ln|x|-17x^3+C

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integral of (29-51x^3)/x

\int \frac{29 - 51 x ^{3}}{x} d x

29 ln ∣ x ∣ - 17 x^{3} + C

Solution steps

\int \frac{29 - 51 x ^{3}}{x} d x

Expand

\frac{29 - 51 x ^{3}}{x} : \frac{29}{x} - 51 x^{2}

= \int \frac{29}{x} - 51 x^{2} 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{29}{x} d x - \int 51 x^{2} d x

\int \frac{29}{x} d x = 29 ln ∣ x ∣

\int 51 x^{2} d x = 17 x^{3}

= 29 ln ∣ x ∣ - 17 x^{3}

Add a constant to the solution

= 29 ln ∣ x ∣ - 17 x^{3} + C

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What is the integral of (29-51x^3)/x ?
The integral of (29-51x^3)/x is 29ln|x|-17x^3+C