Question

what is the integration of this x⁴x² /x²+1​

Answer 1

∫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