What is the integral of (3x^2-7)/(x^3) ?

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

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integral of (3x^2-7)/(x^3)

\int \frac{3 x ^{2} - 7}{x ^{3}} d x

3 ln ∣ x ∣ + \frac{7}{2 x ^{2}} + C

Solution steps

\int \frac{3 x ^{2} - 7}{x ^{3}} d x

Expand

\frac{3 x ^{2} - 7}{x ^{3}} : \frac{3}{x} - \frac{7}{x ^{3}}

= \int \frac{3}{x} - \frac{7}{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{3}{x} d x - \int \frac{7}{x ^{3}} d x

\int \frac{3}{x} d x = 3 ln ∣ x ∣

\int \frac{7}{x ^{3}} d x = - \frac{7}{2 x ^{2}}

= 3 ln ∣ x ∣ - (- \frac{7}{2 x ^{2}})

Simplify

= 3 ln ∣ x ∣ + \frac{7}{2 x ^{2}}

Add a constant to the solution

= 3 ln ∣ x ∣ + \frac{7}{2 x ^{2}} + C

y = x + 2, y = - 1, x = 2, x = 5

9 z - 8

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

\int \frac{x - 7}{x ^{2} - x - 12} d x

\frac{\partial}{\partial x} (8 x e^{5 x y})

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