What is integral x tan e^x dx ??

what is integral x tan e^x dx ??

1 Answer
Jun 16, 2018

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.