Quandaries and Queries


Who is asking: Student
Level: Secondary

Dear Sir,
I need to know that how to solve the integral " e^sin x",
i have tried the substitution method, but to no avail, please help




When you first start to study calculus you use a class of functions that are sometimes called elementary functions. These are the functions that can be build from powers, trig functions and log functions using addition, subtraction, multiplication, division and composition. These are the functions that you learn to differentiate. Unfortunately not every elementary function can be integrated. More precisely, not every elementary function is the derivative of an elementary function. The usual examples of such functions are

ex2sin(x)/x , xx and Sqrt(1-x4)

I am not an expert in this area of mathematics but I am reasonably certain that esin(x) is such a function. I don't think there is an elemantary function whose derivative is esin(x)



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