Answer:
Option B
Explanation:
∫dxx(x4+1)=∫x4+1−x4x(x4+1)dx
=∫x4+1x(x4+1)dx−∫x4x(x4+1)dx
=∫1xdx−∫x3x4+1dx
=log|x|dx−∫x3x4+1dx+C
Let x4+1=t⇒x3dx=dt
⇒ x3dx=14
∴∫dx4(x4+1)=log|x|−14∫dtt+C
= log|x|−14log|t|+C
=log|x|−14log|x4+1|+C
=14log|x4|−14log|x4+1|+C
=14[log|x4|−log|x4+1|+C
=14log(x4x4+1)+C