What is the integral of (4csc^2(t)-3e^t) ?

The integral of (4csc^2(t)-3e^t) is -4cot(t)-3e^t+C

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integral of (4csc^2(t)-3e^t)

\int (4 csc^{2} (t) - 3 e^{t}) d t

- 4 cot (t) - 3 e^{t} + C

Solution steps

\int 4 csc^{2} (t) - 3 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 4 csc^{2} (t) d t - \int 3 e^{t} d t

\int 4 csc^{2} (t) d t = - 4 cot (t)

\int 3 e^{t} d t = 3 e^{t}

= - 4 cot (t) - 3 e^{t}

Add a constant to the solution

= - 4 cot (t) - 3 e^{t} + C

\int e^{3 x} cos (5 x) d x

\int \frac{e ^{l n (x)}}{x} d x

\frac{d}{d x} (5 x + 9)

\frac{d y}{d x} = (x + y + 8)^{2}

y^{^{''}} + 2 y + y = 1

What is the integral of (4csc^2(t)-3e^t) ?
The integral of (4csc^2(t)-3e^t) is -4cot(t)-3e^t+C