What is the integral of cos(x)-3/(x^5) ?

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

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integral of cos(x)-3/(x^5)

\int cos (x) - \frac{3}{x ^{5}} d x

sin (x) + \frac{3}{4 x ^{4}} + C

Solution steps

\int cos (x) - \frac{3}{x ^{5}} 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 cos (x) d x - \int \frac{3}{x ^{5}} d x

\int cos (x) d x = sin (x)

\int \frac{3}{x ^{5}} d x = - \frac{3}{4 x ^{4}}

= sin (x) - (- \frac{3}{4 x ^{4}})

Simplify

= sin (x) + \frac{3}{4 x ^{4}}

Add a constant to the solution

= sin (x) + \frac{3}{4 x ^{4}} + C

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