What is the integral of (x^3+x^2)/(x^5) ?

The integral of (x^3+x^2)/(x^5) is -1/x-1/(2x^2)+C

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integral of (x^3+x^2)/(x^5)

\int \frac{x ^{3} + x ^{2}}{x ^{5}} d x

- \frac{1}{x} - \frac{1}{2 x ^{2}} + C

Solution steps

\int \frac{x ^{3} + x ^{2}}{x ^{5}} d x

Simplify

\frac{x ^{3} + x ^{2}}{x ^{5}} : \frac{x + 1}{x ^{3}}

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

Expand

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

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

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

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

= - \frac{1}{x} - \frac{1}{2 x ^{2}}

Add a constant to the solution

= - \frac{1}{x} - \frac{1}{2 x ^{2}} + C

(x^{4} - 3 x)^{2}

13 x

\int \frac{2 x}{e ^{8 x}} d x

y = - 3 x^{2} - x

\frac{d ^{2}}{d x ^{2}} (\frac{1}{ln ( x )})

What is the integral of (x^3+x^2)/(x^5) ?
The integral of (x^3+x^2)/(x^5) is -1/x-1/(2x^2)+C