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

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

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

\int \frac{( 4 + 3 x ^{2} )}{x ^{3}} d x

- \frac{2}{x ^{2}} + 3 ln ∣ x ∣ + C

Solution steps

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

Expand

\frac{4 + 3 x ^{2}}{x ^{3}} : \frac{4}{x ^{3}} + \frac{3}{x}

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

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

\int \frac{3}{x} d x = 3 ln ∣ x ∣

= - \frac{2}{x ^{2}} + 3 ln ∣ x ∣

Add a constant to the solution

= - \frac{2}{x ^{2}} + 3 ln ∣ x ∣ + C

x \to 16 lim (x)

\frac{\partial}{\partial x} (sin (\frac{1}{1 + y}))

\int_{0}^{4 - x^{2}} x^{2} y d y

\frac{\partial}{\partial x} (x + 5 y)

\frac{x}{3 + x}

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