Writing an integral down is only the first step. A toolkit of techniques can help find its value, from substitutions to trigonometry to partial fractions to differentiation.

If \[f(x)=\int \frac{4x}{x^2-2x-3} dx\] and \(f(0)=15 \ln 3,\) what is the value of \(f(2)?\)

If \(a\) is a nonzero real number, what is \[ \int \frac{35}{x^2 - a^2} dx?\]

**Details and assumptions**

Use \(C\) as the constant of integration.

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