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1. $I=\int f(x)dx$
Đặt: $\sqrt[12]x=t\Rightarrow x=t^{12}\Rightarrow dx=12t^{11}dt$
Từ đó:
$I=\int\frac{t^6.12t^{11}dt}{t^8-t^3}$
$=12\int\frac{t^{14}dt}{t^5-1}$
$=12\int\frac{t^{14}-t^9+t^9-t^4+t^4}{t^5-1}dt$
$=12\int t^9dt+12\int t^4dt+\frac{12}{5}\int\frac{d(t^5-1)}{t^5-1}$
$=\frac{6}{5}t^{10}+\frac{12}{5}t^5+\frac{12}{5}\ln|t^5-1|+C$
$=\frac{6}{5}\sqrt[6]{x^5}+\frac{12}{5}\sqrt[12]{x^5}+\frac{12}{5}\ln|\sqrt[12]{x^5}-1|+C $
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