What is the integral of 1/5 csc^2(x)+1/(x^2) ?

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

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integral of 1/5 csc^2(x)+1/(x^2)

\int \frac{1}{5} csc^{2} (x) + \frac{1}{x ^{2}} d x

- \frac{1}{5} cot (x) - \frac{1}{x} + C

Solution steps

\int \frac{1}{5} csc^{2} (x) + \frac{1}{x ^{2}} 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}{5} csc^{2} (x) d x + \int \frac{1}{x ^{2}} d x

\int \frac{1}{5} csc^{2} (x) d x = - \frac{1}{5} cot (x)

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

= - \frac{1}{5} cot (x) - \frac{1}{x}

Add a constant to the solution

= - \frac{1}{5} cot (x) - \frac{1}{x} + C

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