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Black Advanced Problems in Mathematics

Exam: Black Advanced Problems in Mathematics
Subject: Mathematics
Chapter: Indefinite and Definite Integration

Black Advanced Problems in Mathematics · Mathematics · Indefinite and Definite Integration

∫ ( (f(x)g'(x) - f'(x)g(x))/(f(x)g(x)) ) ( (g(x)) - (f(x))) dx is...

\int \left( \frac{f(x)g'(x) - f'(x)g(x)}{f(x)g(x)} \right) (\log(g(x)) - \log(f(x))) dx

is equal to:

Options

A $\log \left( \frac{g(x)}{f(x)} \right) + C$
B $\frac{1}{2} \left( \log \left( \frac{g(x)}{f(x)} \right) \right)^2 + C$
C $\frac{1}{2} \log \left( \frac{g(x)}{f(x)} \right)^2 + C$
D $\log \left( \frac{g(x)}{f(x)} \right)^2 + C$

Correct answer

C. $\frac{1}{2} \log \left( \frac{g(x)}{f(x)} \right)^2 + C$

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