A Level

MATHEMATICS · Single correct · A Level · Mathematics · Integration · Integration

Problem

\int \frac{dx}{x[(\log x)^2 + 4 \log x - 1]} =

(a)

\frac{1}{2\sqrt{5}} \log \left[ \frac{\log x + 2 - \sqrt{5}}{\log x + 2 + \sqrt{5}} \right] + c

(b)

\frac{1}{\sqrt{5}} \log \left[ \frac{\log x + 2 - \sqrt{5}}{\log x + 2 + \sqrt{5}} \right] + c

(c)

\frac{1}{2\sqrt{5}} \log \left[ \frac{\log x + 2 + \sqrt{5}}{\log x + 2 - \sqrt{5}} \right] + c

(d)

\frac{1}{\sqrt{5}} \log \left[ \frac{\log x + 2 + \sqrt{5}}{\log x + 2 - \sqrt{5}} \right] + c