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

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

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

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

- \frac{3}{5 x ^{5}} + \frac{3}{x ^{2}} + 2 x + C

Solution steps

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

Expand

\frac{3 - 6 x ^{3} + 2 x ^{6}}{x ^{6}} : \frac{3}{x ^{6}} - \frac{6}{x ^{3}} + 2

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

\int \frac{3}{x ^{6}} d x = - \frac{3}{5 x ^{5}}

\int \frac{6}{x ^{3}} d x = - \frac{3}{x ^{2}}

\int 2 d x = 2 x

= - \frac{3}{5 x ^{5}} - (- \frac{3}{x ^{2}}) + 2 x

Simplify

= - \frac{3}{5 x ^{5}} + \frac{3}{x ^{2}} + 2 x

Add a constant to the solution

= - \frac{3}{5 x ^{5}} + \frac{3}{x ^{2}} + 2 x + C

\int 4 x + 2 d x

\int_{0}^{π} sin^{3} (x co) s^{2} x

\int (tan (5 x) + sec (5 x))^{2} d x

\frac{d y}{d x} = (x^{2} - 3 x)^{3}

\frac{1}{x ^{3}}

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