Question

$\int\frac{x\cos x-\sin x}{x^{2}}dx$ is equal to

• A. $\frac{\cos x}{x}+C$
• B. $\frac{\sin 2x}{x}+C$
• C. $\frac{\sin x}{x^{2}}+C$
• D. $\frac{\sin x}{x}+C$
• E. $\frac{\cos 2x}{x}+C$

Hint:

Logic Tip: Whenever you see an integral with $x^2$ in the denominator and a subtraction in the numerator involving $x$ and trigonometric/logarithmic functions, immediately suspect the reverse Quotient Rule. Look at the term *without* the $x$ multiplier in the numerator to identify the original function $u$.

Answer 1

The Correct Option is D