# Integrate: (x^4+x^2+1) dx^2

Solution:

$I=\int (x^{4}+x^{2}+1)dx^{2}\\ \\ Let \hspace{1cm}x^{2}=t\\ \\ \Rightarrow \hspace{1cm}I=\int (t^{2}+t+1)dt\\ \\ \Rightarrow \hspace{1cm}I=\frac{t^{3}}{3}+\frac{t^{2}}{2}+t+c \\ \\ \Rightarrow \hspace{1cm}I=\frac{x^{6}}{3}+\frac{x^{4}}{2}+x^{2}+c$

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