Question

What is integral x tan e^x dx ??

what is integral x tan e^x dx ??

Answer 1

There is no answer in terms of standard functions

Explanation:

We can use integration by parts with `u=x` and `(dv)/(dx)=tane^x` to recast the problem of the integral so that the `x` comes outside of it. Then `(du)/(dx)=1` and `v=inttane^xdx`, so

`int xtane^xdx=x int tan e^xdx-intinttane^xdxdx`

However, we now reach the fundamental issue of the problem - the combination of tan and exponential in this way does not admit an integral solution in any usual way to the problem `inttane^xdx`. Even Wolfram Alpha does not find a solution: http://www.wolframalpha.com/input/?i=integrate+tan+e%5Ex

In the real world, faced with this problem, one would use a numerical scheme to approximate the needed answer.