Integrate the following functions with respect to x : dx 4x+5 - Vidyadip

MCQ

Integrate the following functions with respect to $x : \int\frac{\text{dx}}{4\text{x}+5}$

✓
$\frac{1}{4}\text{ In }(4\text{x}+5)+\text{c}$
B
$\frac{1}{4}\text{ In }(4\text{x}+5)-\text{c}$
C
$\frac{-1}{4}\text{ In }(4\text{x}+5)-\text{c}$
D
$4\text{ In }(4\text{x}-5)-\text{c}$

✓

Answer

Correct option: A.

$\frac{1}{4}\text{ In }(4\text{x}+5)+\text{c}$

$\int\frac{\text{dx}}{4\text{x}+5}=\frac{1}{4}\int\frac{\text{dx}}{\text{x}}$ where $x = 4x + 5$
$=\frac{1}{4}\text{ In }\text{x}+\text{c}_{1}=\frac{1}{4}\text{ In }(4\text{x}+5)+\text{c}_{2}$

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