what is the integration of this x⁴x² /x²+1
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∫x6x2+1dx
=∫(−1x2+1+x4−x2+1)dx
=−∫1x2+1dx+∫x4dx−∫x2dx+∫1dx
∫1x2+1dx
=arctan(x)
∫x4dx
Apply power rule:
∫xndx=xn+1n+1 with n=4:
=x55
x2dx
Apply power rule with n=2:
=x33
Now solving:
∫1dx
Apply constant rule:
=x
Plug in solved integrals:
−∫1x2+1dx+∫x4dx−∫x2dx+∫1dx
=−arctan(x)+x55−x33+x
The problem is solved:
∫x6x2+1dx
=−arctan(x)+x55−x33+x+C
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