Multiplying and dividing the numerator by e we get the given as

⇒ …(1)

Assume e^x + x^e = t

⇒ d(e^x + x^e )=dt

⇒ e^x + ex^{e - 1} = dt

Substituting t and dt in equation 1 we get

⇒

= ln|t| + c

But t = e^x + x^e

∴ ln| e^x + x^e | + c.