# 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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