dx (x-a) (x-b) is equal to: - Vidyadip

MCQ

$\int\frac{\text{dx}}{\sin(\text{x-a})\sin(\text{x-b})}$ is equal to:

A
$\sin(\text{b-a})\log|\frac{\sin(\text{x-b})}{\sin(\text{x-a})}|+\text{c}$
B
$\operatorname{cosec}(\text{b-a})\log|\frac{\sin(\text{x-b})}{\sin(\text{x-b})}|+\text{c}$
✓
$\operatorname{cosec}(\text{b-a})\log|\frac{\sin(\text{x-b})}{\sin(\text{x-a})}|+\text{c}$
D
$\sin(\text{b-a})\log|\frac{\sin(\text{x-a})}{\sin(\text{x-b})}|+\text{c}$

✓

Answer

Correct option: C.

$\operatorname{cosec}(\text{b-a})\log|\frac{\sin(\text{x-b})}{\sin(\text{x-a})}|+\text{c}$

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