+ (1 + 2x) dx is: 1. + c 2. x + c 3. + c 4. + c - Vidyadip

Question

$\int\frac{\sin\text{x} + \cos\text{x}}{\sqrt{(1 + \sin2\text{x})}}\text{dx}$ is:

$\sin\text{x + c}$
$\text{x + c}$
$\cos\text{x + c}$
$\tan\text{x + c}$

✓

Answer

$\text{x + c}$

Solution:

$\int\frac{\sin\text{x} + \cos\text{x}}{\sqrt{(1 + \sin2\text{x})}}\text{dx}$

$\int\frac{\sin\text{x} + \cos\text{x}}{\sqrt{(\sin\text{x}+\cos\text{x})^2}}\text{dx}$

$=\int1\text{dx}$

$=\text{x + c}$

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