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

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

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integral of sin(x)+2e^x

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

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

Solution steps

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

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

\int 2 e^{x} d x = 2 e^{x}

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

Add a constant to the solution

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

\int (- x) d x

\int w e^{5 w + π} d w

\int \frac{e ^{- 3 x}}{3} d x

\int (x^{2} - 7)^{5} (2 x) d x

\int sin^{2} (π) x d x

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