What is the integral of e raised to x cubed?

(ex)3=e3x, so int[(ex)3dx]=int[e3xdx]=e3x/3

the integral ex^3 involves a complex function useful only to integrations such as this known as the exponential integral, or En(x). The integral is:-(1/3)x*E2/3(-x3). To solve this integral, and for more information on the exponential integral, go to http://integrals.wolfram.com/index.jsp?expr=e^(x^3)&random=false