`int (sec^2(theta) - sin(theta)) dtheta` Find the indefinite integral.

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to evaluate the indefinite integral, such that:

`int(sec^2 theta - sin theta) d theta = int sec^2 theta d theta - int sin theta d theta`

`int(sec^2 theta - sin theta) d theta = int 1/(cos^2 theta) d theta + cos theta + c`

You need to remember that `1/(cos^2 theta) = (tan theta)'`

`int(sec^2 theta - sin theta) d theta =tan theta + cos theta + c`

Hence, evaluating the indefinite integral yields `int(sec^2 theta - sin theta) d theta = tan theta + cos theta + c`