Indefinite Integration
Irrational Functions
Grade 12
Question:
<p>Evaluate \(\int \frac{1 + x}{\sqrt{1+x^4}} dx\)</p>
<p>(A) \(\tan^{-1}\sqrt[6]{x} + C\)</p>
<p>(B) \(\ln|x + \sqrt{x + 1}| + C\)</p>
<p>(C) \(\ln\sqrt[6]{x} + \sqrt[6]{x} + C\)</p>
<p>(D) none of these</p>
Step-by-Step Solution
Key Concept: Factor and manipulate the expression to recognize a standard integral form.
<p>This integral requires algebraic manipulation and substitution to simplify the expression under the square root.</p>
Correct Answer: B