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

The integral of ((x+2)^3)/(x^2) is (x^2)/2+6x+12ln|x|-8/x+C

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

\int \frac{( x + 2 ) ^{3}}{x ^{2}} d x

\frac{x ^{2}}{2} + 6 x + 12 ln ∣ x ∣ - \frac{8}{x} + C

Solution steps

\int \frac{( x + 2 ) ^{3}}{x ^{2}} d x

Long division

\frac{( x + 2 ) ^{3}}{x ^{2}} : x + 6 + \frac{12 x + 8}{x ^{2}}

= \int x + 6 + \frac{12 x + 8}{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 x d x + \int 6 d x + \int \frac{12 x + 8}{x ^{2}} d x

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

\int 6 d x = 6 x

\int \frac{12 x + 8}{x ^{2}} d x = 12 ln ∣ x ∣ - \frac{8}{x}

= \frac{x ^{2}}{2} + 6 x + 12 ln ∣ x ∣ - \frac{8}{x}

Add a constant to the solution

= \frac{x ^{2}}{2} + 6 x + 12 ln ∣ x ∣ - \frac{8}{x} + C

\int 0.75 x^{2} d x

\int (6 x^{2} + 5) d x

\int \frac{1 + 3 x + 7 x ^{2} - 2 x ^{3}}{x ^{2}} d x

\int 0.75 (1 - x^{2}) d x

\int ln^{x} (d) x d x

What is the integral of ((x+2)^3)/(x^2) ?
The integral of ((x+2)^3)/(x^2) is (x^2)/2+6x+12ln|x|-8/x+C