First slide

Integration

Question

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

Moderate

A

$\frac{1}{5} \ln (4 x + 5) + c_{2}$
B

$\frac{1}{4} \ln (4 x + 5) + c_{2}$
C

$\ln (4 x + 5) + c_{2}$
D

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

Solution

$\int \frac{d x}{4 x + 5} = \frac{1}{4} \int \frac{d X}{X}, where X = 4 x + 5 = \frac{1}{4} \ln X + c_{1} = \frac{1}{4} \ln (4 x + 5) + c_{2}$

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