`int (csc^2(t) - 2e^t) dt` Find the general indefinite integral.

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Chapter 5, 5.4 - Problem 14 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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gsarora17 | (Level 2) Associate Educator

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`int(csc^2(t)-2e^t)dt` 

Apply the sum rule,

`=intcsc^2(t)dt-int(2e^tdt` 

We now the following common integrals,

`intcsc^2(x)=-cot(x)`  and `inte^xdx=e^x`

evaluate using the above,

`=-cot(t)-2e^t+C`  , C is constant

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