\"\"

\

The function is \"\".

\

Apply derivative on each side with respect to \"\".

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\"\"

\

From the Fundamental Theorem of Calculus part 1:

\

If \"\" is continuous on \"\", then the function \"\" defined by \"\", \"\" is continuous on  \"\" and differentiable on \"\", and  \"\".

\

\"\".

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Therefore the derivative function is always positive.

\

Thus, the function is strictly monotonic and it is an one to one function.

\

\"\"

\

Find \"\".

\

From theorem 5.9:

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\"\".

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\"\".

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Equate \"\" to \"\".

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\"\"

\

\"\"

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Integral property: \"\".

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From the above property we will get \"\".

\

Therefore, \"\".

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\"\".

\

\"\"

\

Substitute \"\" in \"\".

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\"\"

\

Consider \"\".

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\"\".

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Substitute \"\" in \"\".

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\"\"

\

\"\".

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\"\"

\

\"\".