What is the integral of (15000(x-50))/(x^4) ?

The integral of (15000(x-50))/(x^4) is 15000(-1/(2x^2)+(50)/(3x^3))+C

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integral of (15000(x-50))/(x^4)

\int \frac{15000 ( x - 50 )}{x ^{4}} d x

15000 (- \frac{1}{2 x ^{2}} + \frac{50}{3 x ^{3}}) + C

Solution steps

\int \frac{15000 ( x - 50 )}{x ^{4}} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 15000 \cdot \int \frac{x - 50}{x ^{4}} d x

Expand

\frac{x - 50}{x ^{4}} : \frac{1}{x ^{3}} - \frac{50}{x ^{4}}

= 15000 \cdot \int \frac{1}{x ^{3}} - \frac{50}{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

= 15000 (\int \frac{1}{x ^{3}} d x - \int \frac{50}{x ^{4}} d x)

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

\int \frac{50}{x ^{4}} d x = - \frac{50}{3 x ^{3}}

= 15000 (- \frac{1}{2 x ^{2}} - (- \frac{50}{3 x ^{3}}))

Simplify

= 15000 (- \frac{1}{2 x ^{2}} + \frac{50}{3 x ^{3}})

Add a constant to the solution

= 15000 (- \frac{1}{2 x ^{2}} + \frac{50}{3 x ^{3}}) + C

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What is the integral of (15000(x-50))/(x^4) ?
The integral of (15000(x-50))/(x^4) is 15000(-1/(2x^2)+(50)/(3x^3))+C