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Evaluate
Solution:
Consider the given equation above
There are two functions in the given equation which are trigonometric and hyperbolic functions. Since there are two functions in the integration, then we have to integrate the given equation by using Integration by Parts.
If
then
If
then
Using Integration by Parts,
Since the second term of the above equation have two functions, then we have to use the Integration by Parts again.
Consider
If
then
If
then
Again, using by Integration by Parts,
From the first integration by Integration by Parts,
but
Therefore, the final answer is