Oh no

Calculus Level pending

\[\large{\int { \frac { { x }^{ \frac { 1 }{ 4 } }+5 }{ x-16 } dx } =a{ x }^{ \frac { 1 }{ a } }+ b\ln { |{ x }^{ \frac { 1 }{ a } } } -c| + d\ln { |{ x }^{ \frac { 1 }{ a } } } +c| + e\ln { |{ x }^{ \frac { 1 }{ c } } } +a| - a\arctan { \frac { { x }^{ \frac { 1 }{ a } } }{ c } } + C}\]

If integrating the question on LHS gives RHS for some positive integers \(a,b,c,d,e\). Find the value of \(a+b+c+e\). Note \(C\) is an arbitary constant.

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