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

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

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

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

f (x) = 3 x^{2} + 2 x - 4

y = (1 + 5 x)^{9}, (0, 1)

\int \frac{1}{( x + 4 ) ^{2}} d x

x \to 8 lim (\frac{x}{x - 8})

\frac{d y}{d x} y = (x^{2} + 1)^{3}

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