What is the integral of ((csc(y))^2-sec(y)tan(y)) ?

The integral of ((csc(y))^2-sec(y)tan(y)) is -cot(y)-sec(y)+C

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integral of ((csc(y))^2-sec(y)tan(y))

\int ((csc (y))^{2} - sec (y) tan (y)) d y

- cot (y) - sec (y) + C

Solution steps

\int (csc (y))^{2} - sec (y) tan (y) d y

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int (csc (y))^{2} d y - \int sec (y) tan (y) d y

\int (csc (y))^{2} d y = - cot (y)

\int sec (y) tan (y) d y = sec (y)

= - cot (y) - sec (y)

Add a constant to the solution

= - cot (y) - sec (y) + C

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\int_{- 6}^{0} (\frac{y}{6} + y + 7) d y

What is the integral of ((csc(y))^2-sec(y)tan(y)) ?
The integral of ((csc(y))^2-sec(y)tan(y)) is -cot(y)-sec(y)+C