Integrate sin(2sinh(3x)): Solutions & Tips

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The integral ∫sin(2sinh(3x)) was approached using a u substitution, letting u=3x, which simplifies it to 1/3∫sin(2sinh(u)). However, the challenge remains in eliminating the sinh function, with attempts made to use exponential forms and identities. It is noted that this integral may not have an anti-derivative expressible in elementary functions. The origin of the integral is questioned, suggesting that context may provide further insights into its complexity. Understanding the limitations of the integral's solvability is crucial for further progress.
anthonybommarito1
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Homework Statement



∫sin(2sinh(3x))

Homework Equations

The Attempt at a Solution


okay so i did a u substitution letting u=3x so we get 1/3∫sin(2sinh(u)) but i have no idea how to get rid of the sinh, i tried writing in exponential form or maybe i have to use some identity.. I am not sure where to go from there!
 
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anthonybommarito1 said:

Homework Statement



∫sin(2sinh(3x))

Homework Equations

The Attempt at a Solution


okay so i did a u substitution letting u=3x so we get 1/3∫sin(2sinh(u)) but i have no idea how to get rid of the sinh, i tried writing in exponential form or maybe i have to use some identity.. I am not sure where to go from there!
You should always include the dx or whatever when writing an integral.

It's not clear this integral even has an anti-derivative which can be expressed in terms of elementary functions.

Where does this integral come from?
 

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