The indefinite integral ∫ e ^ e ^ x ( x e ^ x ⋅ ln x + 1 x )dx...

Given integral is $I = ∫$\left({e}^{{e}^{x}} ⋅ {e}^{x} ⋅ ln x + \dfrac{{e}^{{e}^{x}}}{x}\right)dx$<br />Let,${e}^{{e}^{x}} = f\left(x\right)$and$ln x = g\left(x\right)$<br />$∴ I = ∫ \left({f}^{'}\left(x\right)g\left(x\right) + f\left(x\right){g}^{'}\left(x\right)\right)dx$<br />$= f\left(x\right) \cdot g\left(x\right) + c$<br />$= {e}^{{e}^{x}} ⋅ ln x + c