What is $\smallint \frac{{{{\rm{x}}^4} - 1{\rm{\;}}}}{{{{\rm{x}}^2}\sqrt {{{\rm{x}}^4} + {{\rm{x}}^2} + 1} }}{\rm{dx}}$ equal to?

Question

What is $\smallint \frac{{{{\rm{x}}^4} - 1{\rm{\;}}}}{{{{\rm{x}}^2}\sqrt {{{\rm{x}}^4} + {{\rm{x}}^2} + 1} }}{\rm{dx}}$ equal to?

TuteeHUB · Accepted Answer

$\sqrt {\frac{{{{\rm{x}}^4} - {{\rm{x}}^2} + 1}}{{\rm{x}}} + {\rm{c}}} $

TuteeHUB · Answer

$\sqrt {\frac{{{{\rm{x}}^4} + {{\rm{x}}^2} + 1}}{{\rm{x}}}} + {\rm{c}}$

TuteeHUB · Answer

$\sqrt {{{\rm{x}}^4} + 2 - \frac{1}{{{{\rm{x}}^2}}}} + {\rm{c}}$

TuteeHUB · Answer

$\sqrt {{{\rm{x}}^2} + \frac{1}{{{{\rm{x}}^2}}} + 1} + {\rm{c}}$

1.	What is \(\smallint \frac{{{{\rm{x}}^4} - 1{\rm{\;}}}}{{{{\rm{x}}^2}\sqrt {{{\rm{x}}^4} + {{\rm{x}}^2} + 1} }}{\rm{dx}}\) equal to?
A.	\(\sqrt {\frac{{{{\rm{x}}^4} + {{\rm{x}}^2} + 1}}{{\rm{x}}}} + {\rm{c}}\)
B.	\(\sqrt {{{\rm{x}}^4} + 2 - \frac{1}{{{{\rm{x}}^2}}}} + {\rm{c}}\)
C.	\(\sqrt {{{\rm{x}}^2} + \frac{1}{{{{\rm{x}}^2}}} + 1} + {\rm{c}}\)
D.	\(\sqrt {\frac{{{{\rm{x}}^4} - {{\rm{x}}^2} + 1}}{{\rm{x}}} + {\rm{c}}} \)
Answer» D. \(\sqrt {\frac{{{{\rm{x}}^4} - {{\rm{x}}^2} + 1}}{{\rm{x}}} + {\rm{c}}} \)

What is \(\smallint \frac{{{{\rm{x}}^4} - 1{\rm{\;}}}}{{{{\rm{x}}^2}\sqrt {{{\rm{x}}^4} + {{\rm{x}}^2} + 1} }}{\rm{dx}}\) equal to?