Question

find the indefinite integral of 1/2x+3 dx​

Answer 1

Given :

The function is $\tt f(x) = \frac{1}{2x + 3}$

To Find :

$\tt \int \frac{1}{2x + 3} \: \: dx$

Solution :

Let , 2x + 3 = t

Differentiating t wrt x , we get

2 = dt/dx => dx = dt/2

Thus ,

$\tt \implies \tt \int \frac{1}{2x + 3} \: \: dx$

$\tt \implies \tt \int \frac{1}{2t} \: \: dt$

$\tt \implies \frac{1}{2} \tt \int \frac{1}{t} \: \: dt$

$\tt \implies \frac{1}{2} \times log(t)$

$\tt \implies \frac{1}{2} \times log(2x + 3)$

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