Question

The integral $I=\int \frac{1}{x \cdot \sec x}-\ln x^{\sin x} d x$ simplifies to (where, $c$ is the constant of integration)

• A. $\ln x \sin x+c$
• B. $\ln x \cos x+c$
• C. $x \ln \sin x+c$
• D. $x \ln \cos x+c$

Answer 1

Answer: (B)

Given $I=\int \cos x \cdot \frac{1}{x}+-\sin x \ln x d x$ Since, $\int f \cdot g^{\prime}+f^{\prime} g d x$
$=f \cdot g+c $
$\Rightarrow I=\cos x \ln x+c$