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Indefinite Integration — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsIndefinite Integration2 Marks
Question
Evaluate:
$\int \frac{4 x+3}{2 x+1} \cdot d x$
✓

Answer

$ \int \frac{4 x+3}{2 x+1} d x $
$ =  \int \frac{2(2 x+1)+1}{2 x+1} d x$
$=\int\left(\frac{2(2 x+1)}{2 x+1}+\frac{1}{2 x+1}\right) d x$
$=2 \int 1 d x+\int \frac{1}{2 x+1} d x$
$=2 x+\frac{1}{2} \log |2 x+1|+c .$

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