Summer of 69!

Calculus Level 4

\[ \large \int { { (x+\sqrt { { x }^{ 2 }+1 } ) }^{ 69 } } dx\]

If the indefinite integral above is of the form:

\[ \large \frac { a }{ b } \left[ \frac { { (x+\sqrt { { x }^{ 2 }+1 } ) }^{ c } }{ c } +\frac { { (x+\sqrt { { x }^{ 2 }+1 } ) }^{ d } }{ d } \right] +\alpha\]

where \(\alpha \) is constant of integration.

\(c > d\)

Find \(a+b+c-d\).

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