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

The integral of (2x^4-x^2)/(x^3) is x^2-ln|x|+C

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integral of (2x^4-x^2)/(x^3)

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

x^{2} - ln ∣ x ∣ + C

Solution steps

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

Expand

\frac{2 x ^{4} - x ^{2}}{x ^{3}} : 2 x - \frac{1}{x}

= \int 2 x - \frac{1}{x} 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 2 x d x - \int \frac{1}{x} d x

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

\int \frac{1}{x} d x = ln ∣ x ∣

= x^{2} - ln ∣ x ∣

Add a constant to the solution

= x^{2} - ln ∣ x ∣ + C

\int \frac{t - 1}{t} d t

\int \frac{9 x ^{3} - 8 x + 5}{x ^{3} - x ^{2}} d x

\int e^{- 3 x} (- 3 x) d x

\int \frac{1}{z ( z + 1 ) ^{2}} d z

\int \frac{a ^{2} + b}{b - a x} d x

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