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

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

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integral of (5/x-2x^3)

\int (\frac{5}{x} - 2 x^{3}) d x

5 ln ∣ x ∣ - \frac{x ^{4}}{2} + C

Solution steps

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

\int \frac{5}{x} d x = 5 ln ∣ x ∣

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

= 5 ln ∣ x ∣ - \frac{x ^{4}}{2}

Add a constant to the solution

= 5 ln ∣ x ∣ - \frac{x ^{4}}{2} + C

\frac{d y}{d x} - e^{5 x + y} = 0

\frac{d}{d x} (\frac{- 15}{x})

\frac{\partial}{\partial x} (sin (x yz))

\frac{d}{d x} (2 sin (- x))

34 (3 p + 1)^{- \frac{2}{5}}

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