Question Bank [2022] — Maths STD 12 Science — Question
Maharashtra BoardEnglish MediumSTD 12 ScienceMathsQuestion Bank [2022]2 Marks
Question
$\int \frac{1}{4 x+5 x^{-11}} d x$
✓
Answer
$ \text { Let } I =\int \frac{1}{4 x+5 x^{-11}} d x$
$=\int \frac{1}{4 x+\frac{5}{x^{11}}} d x$
$=\int \frac{x^{11}}{4 x^{12}+5} d x $
Put $4 x ^{12}+5= t$
Differentiating w.r.t. $x$, we get
$ 4(12) x ^{11} dx = dt$
$\therefore x ^{11} dx =\frac{1}{48} dt$
$\therefore I =\frac{1}{48} \int \frac{ dt }{ t }$
$=\frac{1}{48} \log | t |+ c$
$\therefore I =\frac{1}{48} \log \left|4 x^{12}+5\right|+ c $
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