What is the integral of (3sin(y)-2sec^2(y)) ?

The integral of (3sin(y)-2sec^2(y)) is -3cos(y)-2tan(y)+C

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integral of (3sin(y)-2sec^2(y))

\int (3 sin (y) - 2 sec^{2} (y)) d y

- 3 cos (y) - 2 tan (y) + C

Solution steps

\int 3 sin (y) - 2 sec^{2} (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 3 sin (y) d y - \int 2 sec^{2} (y) d y

\int 3 sin (y) d y = - 3 cos (y)

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

= - 3 cos (y) - 2 tan (y)

Add a constant to the solution

= - 3 cos (y) - 2 tan (y) + C

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What is the integral of (3sin(y)-2sec^2(y)) ?
The integral of (3sin(y)-2sec^2(y)) is -3cos(y)-2tan(y)+C