What is the integral of (-2x^7-4x^4)/(x^5) ?

The integral of (-2x^7-4x^4)/(x^5) is -(2x^3)/3-4ln|x|+C

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integral of (-2x^7-4x^4)/(x^5)

\int \frac{- 2 x ^{7} - 4 x ^{4}}{x ^{5}} d x

- \frac{2 x ^{3}}{3} - 4 ln ∣ x ∣ + C

Solution steps

\int \frac{- 2 x ^{7} - 4 x ^{4}}{x ^{5}} d x

Expand

\frac{- 2 x ^{7} - 4 x ^{4}}{x ^{5}} : - 2 x^{2} - \frac{4}{x}

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

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

\int \frac{4}{x} d x = 4 ln ∣ x ∣

= - \frac{2 x ^{3}}{3} - 4 ln ∣ x ∣

Add a constant to the solution

= - \frac{2 x ^{3}}{3} - 4 ln ∣ x ∣ + C

\int_{0}^{2} π (2 x - x^{2})^{2} d x

\frac{d}{d x} (e^{x} cos (6 x))

\int_{- 1}^{3} (x^{3} + 5 x) d x

y \to \infty lim (e^{y})

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

What is the integral of (-2x^7-4x^4)/(x^5) ?
The integral of (-2x^7-4x^4)/(x^5) is -(2x^3)/3-4ln|x|+C