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

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

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

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

\int \frac{x sin ( x )}{cos ( x )} d x

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

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

\int \frac{1}{3} e^{3 y} d y

\int (e^{y} - e^{2 x}) d x

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