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

\frac{1}{4} ln (4 x + 5) + c

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\frac{1}{4} ln (4 x + 5) - c

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\frac{- 1}{4} ln (4 x + 5) - c

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4 ln (4 x - 5) - c

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Solution

The correct options are
A $\frac{1}{4} ln (4 x + 5) + c$
D $\frac{1}{4} ln (4 x + 5) - c$
$\int \frac{d x}{4 x + 5} = \frac{1}{4} \int \frac{d X}{X}$ where $X = 4 x + 5$
$= \frac{1}{4} ln X + c_{1} = \frac{1}{4} ln (4 x + 5) + c_{2}$

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