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

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

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

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

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

Solution steps

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

\int 3 sin (x) d x = - 3 cos (x)

\int 2 d x = 2 x

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

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

Add a constant to the solution

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

f (x) = 4 x (1 - x), g (x) = 4 x - 4

\frac{d}{d x} (\frac{6 x ^{3} - 5 x ^{2} - 2 x}{4 x - 3 x ^{2}})

\frac{d}{d x} (5 x + \frac{100}{x})

x \to 2 lim (\frac{x + 2}{x - 2})

\frac{d}{d x} (\frac{5}{3})

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