Are sine and cosine missing?

Calculus Level 5

1tan(x)+cot(x)+sec(x)+csc(x)dx\large \int \dfrac{1}{\tan (x) + \cot (x )+ \sec (x) + \csc( x)} \, dx

If the indefinite integral above equals to cos(x)a+sin(x)b+xc \dfrac{\cos (x)}{a} + \dfrac{\sin (x)}{b} + \dfrac{x}{c} for constants a,ba,b and cc, what is the value of a+b+ca + b + c?

Assume we ignore the arbitrary constant of integration.

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