What is the integral of ((19.8)/x-9x^2) ?

The integral of ((19.8)/x-9x^2) is 19.8ln|x|-3x^3+C

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integral of ((19.8)/x-9x^2)

\int (\frac{19.8}{x} - 9 x^{2}) d x

19.8 ln ∣ x ∣ - 3 x^{3} + C

Solution steps

\int \frac{19.8}{x} - 9 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 \frac{19.8}{x} d x - \int 9 x^{2} d x

\int \frac{19.8}{x} d x = 19.8 ln ∣ x ∣

\int 9 x^{2} d x = 3 x^{3}

= 19.8 ln ∣ x ∣ - 3 x^{3}

Add a constant to the solution

= 19.8 ln ∣ x ∣ - 3 x^{3} + C

y^{^{''}} + 8 y^{^{'}} + 20 y = 0, y (0) = 0, y^{^{'}} (0) = 0

\int_{1}^{2} x (2 - x) d x

\int_{0}^{1} \frac{85}{x ^{5}} d x

\frac{d}{d x} (\frac{x}{9 + x})

f (x) = x^{2} + 10

What is the integral of ((19.8)/x-9x^2) ?
The integral of ((19.8)/x-9x^2) is 19.8ln|x|-3x^3+C