Integrate the following w.r.t x : 1 2 x + 3 Options: A . &nbspln |2x + 3| + c B . &nbspln|2x+3|2+c C . &nbspln(2x+3)2x+3+c D . &nbspNone of these

Answer: Option B : B Let u = 2 x + 3 ⇒ d u d x = 2 ⇒ d x = d u 2 I = ∫ y d x = ∫ d x 2 x + 3 = ∫ 1 u × d u 2 = 1 2 ∫ d u u = 1 2 l n u + c = 1 2 l n | 2 x + 3 | + c

Integrate the following w.r.t x:12x+3

Question

Integrate the following w.r.t

x : \frac{1}{2 x + 3}

Options:

A . ln |2x + 3| + c

B . ln|2x+3|2+c

C . ln(2x+3)2x+3+c

D . None of these

Answer: Option B
:
B
Let

u = 2 x + 3

\Rightarrow \frac{d u}{d x} = 2

\Rightarrow d x = \frac{d u}{2}

I = \int y d x = \int \frac{d x}{2 x + 3} = \int \frac{1}{u} \times \frac{d u}{2}

\frac{1}{2} \int \frac{d u}{u}

\frac{1}{2} l n u + c

\frac{1}{2} l n | 2 x + 3 | + c

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