What is the integral of (1+x^2)/(x^3) ?

The integral of (1+x^2)/(x^3) is -1/(2x^2)+ln|x|+C

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integral of (1+x^2)/(x^3)

\int \frac{1 + x ^{2}}{x ^{3}} d x

- \frac{1}{2 x ^{2}} + ln ∣ x ∣ + C

Solution steps

\int \frac{1 + x ^{2}}{x ^{3}} d x

Expand

\frac{1 + x ^{2}}{x ^{3}} : \frac{1}{x ^{3}} + \frac{1}{x}

= \int \frac{1}{x ^{3}} + \frac{1}{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{1}{x ^{3}} d x + \int \frac{1}{x} d x

\int \frac{1}{x ^{3}} d x = - \frac{1}{2 x ^{2}}

\int \frac{1}{x} d x = ln ∣ x ∣

= - \frac{1}{2 x ^{2}} + ln ∣ x ∣

Add a constant to the solution

= - \frac{1}{2 x ^{2}} + ln ∣ x ∣ + C

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

cos (\frac{x}{2})

\int \frac{1}{e ^{5 x}} d x

\int - 7 x^{- 8} d x

y = 5 csc (x) + 7 cos (x)

What is the integral of (1+x^2)/(x^3) ?
The integral of (1+x^2)/(x^3) is -1/(2x^2)+ln|x|+C