What is the integral of ax^3+6/(x^2) ?

The integral of ax^3+6/(x^2) is (ax^4)/4-6/x+C

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integral of ax^3+6/(x^2)

\int a x^{3} + \frac{6}{x ^{2}} d x

\frac{a x ^{4}}{4} - \frac{6}{x} + C

Solution steps

\int a x^{3} + \frac{6}{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 a x^{3} d x + \int \frac{6}{x ^{2}} d x

\int a x^{3} d x = \frac{a x ^{4}}{4}

\int \frac{6}{x ^{2}} d x = - \frac{6}{x}

= \frac{a x ^{4}}{4} - \frac{6}{x}

Add a constant to the solution

= \frac{a x ^{4}}{4} - \frac{6}{x} + C

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What is the integral of ax^3+6/(x^2) ?
The integral of ax^3+6/(x^2) is (ax^4)/4-6/x+C