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

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

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integral of 2csc^2(x)-3e^x

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

- 2 cot (x) - 3 e^{x} + C

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 2 csc^{2} (x) d x - \int 3 e^{x} d x

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

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

= - 2 cot (x) - 3 e^{x}

Add a constant to the solution

= - 2 cot (x) - 3 e^{x} + C

\int 2 x + \frac{1}{x ^{2}} d x

\int \frac{x - x ^{2}}{x} d x

\int \frac{5 x - 15}{( x ^{2} + 2 x + 4 ) ^{2}} d x

\int x (1 + x)^{4} d x

\int \frac{3 x + 5}{x ^{2} - 3 x + 2} d x

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