Math problem

Given is the function:

f(x) = e^{(pi/2)i[(e^lnx)+1]}

where e is the base of the natural logarithm e=2.718

i=sqrt(-1)

and pi=3.14

Find the antiderivative(s) of f(x)...I found two different forms using two different methods.Prove your results.Have fun!

Here's one way to do it:

f(x) = e^{(pi/2)i[(e^lnx)+1]}=e^{(pi/2)i(x+1)}=e^(pi*i/2)*e^(pi*i*x/2)

pi*i/2=n

f(x)=n*e^(nx)

u substitution, u=nx

F(x)=e^u+C=e^(nx)+C=e^(x*pi*i/2)+C=[e^(pi*i)]^(x/2)=(-1)^(x/2)=i^x+C

Very simple answer from a complicated question.  Reminds me of my math tests.

Sorry,but I have to say that it is incorrect:

you said that pi*i/2=n but when you substituted this value in e^(pi*i/2)*e^(pi*i*x/2) you forgot that n is the power of e in the first term as well, it should be (e^n)*(e^nx) which is also simple to integrate