Hello helloboys2017,

Well, It is pleasant to see such a tricky and Do Not Solve type of question:

We can't actually integrate the functions, as all the examples of type e^(X^2) or e^sinx, e^cos, e^(sin^2(x)) etc... can't be integrated, but still if you need to know how to actually know why they can't be integrated then you can refer to :

One symbolic way to do it is to use infinite series  . Since ex=1+x+x22!+x33!+=1+x+x22+x36+ (for all x ), it follows that ex2=1+x2+x42+x66+ (for all x ).

It is valid in this example to now integrate term-by-term (the result is true for all x ):

∫ex2dx=∫(1+x2+x42+x66+)dx

=C+x+x33+x510+x742+ .

Alternatively, you can also give the antiderivative a name. Wolfram Alpha writes the antiderivative whose graph goes through the origin as √π2erfi(x) , where erfi(x) is called the "imaginary error function".

Good Luck, and keep learning...

Hope this helps, and feel free to ask any further query...

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Have a great eve!