What is the integral of (5csc^2(t)-6e^t) ?

The integral of (5csc^2(t)-6e^t) is -5cot(t)-6e^t+C

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integral of (5csc^2(t)-6e^t)

\int (5 csc^{2} (t) - 6 e^{t}) d t

- 5 cot (t) - 6 e^{t} + C

Solution steps

\int 5 csc^{2} (t) - 6 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 5 csc^{2} (t) d t - \int 6 e^{t} d t

\int 5 csc^{2} (t) d t = - 5 cot (t)

\int 6 e^{t} d t = 6 e^{t}

= - 5 cot (t) - 6 e^{t}

Add a constant to the solution

= - 5 cot (t) - 6 e^{t} + C

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What is the integral of (5csc^2(t)-6e^t) ?
The integral of (5csc^2(t)-6e^t) is -5cot(t)-6e^t+C