Question

Evaluate: \[ \int \frac{x^2}{1 + (x^3)^2} \, dx \] 

• A. \( \tan^{-1} x^{2} + c \)
• B. \( \frac{2}{3} \tan^{-1} x^{3} + c \)
• C. \( \frac{1}{3} \tan^{-1} (x^{3}) + c \)
• D. \( \frac{1}{2} \tan^{-1} x^{2} + c \)
• E. \( \tan^{-1} x^{3} + c \)

Hint:

When you see a power of $x$ in the numerator that is exactly one less than the power inside a bracket in the denominator, substitution is almost always the intended path.

Answer 1

The Correct Option is C