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

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

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

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

\int \frac{5 e ^{\frac{13}{x}}}{x ^{2}} d x

\int (x + 2) x d x

\int 2 sin (7 x) d x

\int \frac{3}{3 + x} d x

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

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