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

The integral of sin(e^x) is \Si(e^x)+C

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integral of sin(e^x)

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

Si (e^{x}) + C

Solution steps

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

Apply u-substitution

= \int \frac{sin ( u )}{u} d u

Use the nonelementary integral:

\int \frac{sin ( x )}{x} d x = Si (x)

= Si (u)

Substitute back

u = e^{x}

= Si (e^{x})

Add a constant to the solution

= Si (e^{x}) + C

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