What is the integral of (1/(x^2)-sin(x)) ?

The integral of (1/(x^2)-sin(x)) is -1/x+cos(x)+C

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integral of (1/(x^2)-sin(x))

\int (\frac{1}{x ^{2}} - sin (x)) d x

- \frac{1}{x} + cos (x) + C

Solution steps

\int \frac{1}{x ^{2}} - sin (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 ^{2}} d x - \int sin (x) d x

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

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

= - \frac{1}{x} - (- cos (x))

Simplify

= - \frac{1}{x} + cos (x)

Add a constant to the solution

= - \frac{1}{x} + cos (x) + C

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