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

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

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

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

2 ln ∣ x ∣ - \frac{3}{2 x ^{2}} + C

Solution steps

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

Expand

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

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

\int \frac{2}{x} d x = 2 ln ∣ x ∣

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

= 2 ln ∣ x ∣ - \frac{3}{2 x ^{2}}

Add a constant to the solution

= 2 ln ∣ x ∣ - \frac{3}{2 x ^{2}} + C

\frac{\partial}{\partial x} (2 x^{2} y - x^{3})

n = 1 \sum \infty \frac{2}{3 ^{n + 1}}

\frac{1}{S}

\int \frac{( 4 - 2 x )}{( x + 1 ) ( x - 1 ) ^{2}} d x

\int_{1}^{\infty} \frac{3}{x ^{2}} d x

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