\(\int (brain ) +(brain)^2d(brain)\)

Calculus Level 5

Given

\[I_{a}=\int_{1.0002014}^{e}\left[\frac{(\cos(a\ln x)(1-x\ln x)}{(x(\ln x)^{2})}+\frac{a\sin a\ln x}{x\ln x}\right]\exp x dx\]

and

\[I_{10^{7}}-I_{0} =\frac{\exp b\cos h}{i}-\frac{\exp d}{f}[1-\cos10^{7}] -\frac{\exp b}{c},\]

find the value of

\[\left[\frac{h(b-c)}{df}\right].\]

Note: [.] is the greatest integer function.

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