Integration Month

Calculus Level 4

tan1(x)x4dx \large \int \frac{\tan^{-1}(x)}{x^4} \, dx

If the indefinite integral above equals to tan1(x)axa+bcln(xd+bxd)bcxd+C - \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,ca,b,c and dd with b,cb,c coprime and arbitrary constant CC, find the value of a+b+c+da+b+c+d.

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