Question

The integral \[ \int \frac{x^2}{1+x^6}\,dx \] is equal to:

• A. $x^{3} + C$
• B. $\frac{1}{3} \text{Tan}^{-1}(x^{3}) + C$
• C. $\log(1+x^{3})$
• D. $\frac{1}{1+x^{3}} + C$

Hint:

Whenever the power in the denominator is twice the power in the numerator plus one (excluding the constant), consider an inverse trigonometric substitution.

Answer 1

The Correct Option is B