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

The integral of 2sin(x)-3e^x is -2cos(x)-3e^x+C

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

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

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

Solution steps

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

\int 2 sin (x) d x = - 2 cos (x)

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

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

Add a constant to the solution

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

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

\int x^{\frac{2}{3}} ln (x) d x

\int \frac{- 3}{1 - x ^{2}} d x

\int - \frac{2}{x - 1} d x

\int \frac{x + 1}{x ^{2} - 2 x - 8} d x

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