Question
Integrate the following functions w.r.t. x:
$\frac{1}{4 x+5 x^{-11}}$
$\frac{1}{4 x+5 x^{-11}}$
$=\int \frac{x^{11}}{x^{11}\left(4 x+5 x^{-11}\right)} d x$
$=\int \frac{x^{11}}{4 x^{12}+5} d x$
$=\frac{1}{48} \int \frac{48 x^{11}}{4 x^{12}+5} d x$
$=\frac{1}{48} \int \frac{\frac{d}{d x}\left(4 x^{12}+5\right)}{4 x^{12}+5} d x$
$=\frac{1}{48} \log \left|4 x^{12}+5\right|+c \ldots\left[\because \int \frac{f^{\prime}(x)}{f(x)} d x=\log |f(x)|+c\right]$
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$\log _e(9.01)$, given that $\log 3=1.0986$.