What is the integral of 3x^4-5/(x^2)+6 ?

The integral of 3x^4-5/(x^2)+6 is (3x^5)/5+5/x+6x+C

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integral of 3x^4-5/(x^2)+6

\int 3 x^{4} - \frac{5}{x ^{2}} + 6 d x

\frac{3 x ^{5}}{5} + \frac{5}{x} + 6 x + C

Solution steps

\int 3 x^{4} - \frac{5}{x ^{2}} + 6 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 3 x^{4} d x - \int \frac{5}{x ^{2}} d x + \int 6 d x

\int 3 x^{4} d x = \frac{3 x ^{5}}{5}

\int \frac{5}{x ^{2}} d x = - \frac{5}{x}

\int 6 d x = 6 x

= \frac{3 x ^{5}}{5} - (- \frac{5}{x}) + 6 x

Simplify

= \frac{3 x ^{5}}{5} + \frac{5}{x} + 6 x

Add a constant to the solution

= \frac{3 x ^{5}}{5} + \frac{5}{x} + 6 x + C

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What is the integral of 3x^4-5/(x^2)+6 ?
The integral of 3x^4-5/(x^2)+6 is (3x^5)/5+5/x+6x+C