# Integration Month

Calculus Level 4

$\large \int \frac{\tan^{-1}(x)}{x^4} \, dx$

If the indefinite integral above equals to $- \frac{\tan^{-1}(x)}{a\cdot x^a} + \frac bc \ln \left( \frac{x^d+b}{x^d} \right) - \frac b{c\cdot x^d} + C$

for positive integer constants $a,b,c$ and $d$ with $b,c$ coprime and arbitrary constant $C$, find the value of $a+b+c+d$.

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