What is the integral of 5e^x+3sin(x) ?

The integral of 5e^x+3sin(x) is 5e^x-3cos(x)+C

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integral of 5e^x+3sin(x)

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

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

Solution steps

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

\int 5 e^{x} d x = 5 e^{x}

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

= 5 e^{x} - 3 cos (x)

Add a constant to the solution

= 5 e^{x} - 3 cos (x) + C

\int \frac{1}{x 4 x ^{2} + 49} d x

\frac{d}{d x} (- 27 e^{- 3 x})

\frac{d}{d x} (e^{- 0.01 x})

\int 12 t d t

2^{(5 x)}

What is the integral of 5e^x+3sin(x) ?
The integral of 5e^x+3sin(x) is 5e^x-3cos(x)+C