Integrating sin(x) exp(sin(x))

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In summary, the formula for integrating sin(x) exp(sin(x)) is ∫sin(x)exp(sin(x))dx = -exp(cos(x)) + C, where C is the constant of integration. To solve the integral of sin(x) exp(sin(x)), you can use integration by parts. No, substitution is not a suitable method for evaluating the integral of sin(x) exp(sin(x)) and instead, a graphing calculator or software can be used to graph the function. While there is an indefinite integral for sin(x) exp(sin(x)), the definite integral must be evaluated numerically.
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james7henderso
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Hello Physics Forum,

I am trying to find an analytic solution to an equation of the form ∫sin(x/a) exp(b sin(x/a)) dx. I have tried integration by parts and all the usual tricks but can't seem to get anywhere

Thanks in advance for your help

James
 
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You can express the undefined integral on the form of an infinite series, but not on a closed form with the elementary and current special functions.
 

1. What is the formula for integrating sin(x) exp(sin(x))?

The formula for integrating sin(x) exp(sin(x)) is ∫sin(x)exp(sin(x))dx = -exp(cos(x)) + C, where C is the constant of integration.

2. How do you solve the integral of sin(x) exp(sin(x))?

To solve the integral of sin(x) exp(sin(x)), you can use integration by parts. Let u = sin(x) and dv = exp(sin(x))dx. Then, du = cos(x)dx and v = exp(sin(x)). Substituting these values into the integration by parts formula, ∫u*dv = uv - ∫v*du, we get ∫sin(x)exp(sin(x))dx = -exp(cos(x)) + C as the solution.

3. Can the integral of sin(x) exp(sin(x)) be evaluated using substitution?

No, substitution is not a suitable method for evaluating the integral of sin(x) exp(sin(x)) as it does not lead to a simpler expression or make the integration easier.

4. How do you graph the function sin(x) exp(sin(x))?

To graph the function sin(x) exp(sin(x)), you can use a graphing calculator or graphing software. Simply enter the function into the calculator or software and adjust the domain and range as desired to see the graph.

5. Is there an indefinite integral for sin(x) exp(sin(x))?

Yes, the indefinite integral for sin(x) exp(sin(x)) is -exp(cos(x)) + C, where C is the constant of integration. However, the definite integral of this function cannot be expressed in terms of elementary functions and must be evaluated numerically.

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