What is the integral of (5x^2+2)/(x^4) ?

The integral of (5x^2+2)/(x^4) is -5/x-2/(3x^3)+C

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integral of (5x^2+2)/(x^4)

\int \frac{5 x ^{2} + 2}{x ^{4}} d x

- \frac{5}{x} - \frac{2}{3 x ^{3}} + C

Solution steps

\int \frac{5 x ^{2} + 2}{x ^{4}} d x

Expand

\frac{5 x ^{2} + 2}{x ^{4}} : \frac{5}{x ^{2}} + \frac{2}{x ^{4}}

= \int \frac{5}{x ^{2}} + \frac{2}{x ^{4}} 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{5}{x ^{2}} d x + \int \frac{2}{x ^{4}} d x

\int \frac{5}{x ^{2}} d x = - \frac{5}{x}

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

= - \frac{5}{x} - \frac{2}{3 x ^{3}}

Add a constant to the solution

= - \frac{5}{x} - \frac{2}{3 x ^{3}} + C

\int_{1}^{2} 2 x^{2} x^{3} + 1 d x

\frac{d}{d x} (\frac{e ^{x}}{sin ( 2 x )})

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

x \to 0 lim (\frac{sin ( x )}{- x})

What is the integral of (5x^2+2)/(x^4) ?
The integral of (5x^2+2)/(x^4) is -5/x-2/(3x^3)+C