What is the integral of csc^2(t)-2e^t ?

The integral of csc^2(t)-2e^t is -cot(t)-2e^t+C

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integral of csc^2(t)-2e^t

\int csc^{2} (t) - 2 e^{t} d t

- cot (t) - 2 e^{t} + C

Solution steps

\int csc^{2} (t) - 2 e^{t} d t

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^{2} (t) d t - \int 2 e^{t} d t

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

\int 2 e^{t} d t = 2 e^{t}

= - cot (t) - 2 e^{t}

Add a constant to the solution

= - cot (t) - 2 e^{t} + C

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\frac{900}{s ^{2} + 90 s + 900}

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\int_{0}^{x} e^{- u} d u

What is the integral of csc^2(t)-2e^t ?
The integral of csc^2(t)-2e^t is -cot(t)-2e^t+C