NCERT Class 12 · Ch 7 Miscellaneous Exercise · Q12
NCERT Class 12 Maths · Chapter 7 Integrals · Miscellaneous Exercise Question 12
Evaluate \(\int \frac{x^{3}}{\sqrt{1 - x^{8}}}\, dx\).
💡 Concept Hints
- Identify the domain and the inner and outer functions, or the relevant one-sided limits.
- Apply the appropriate differentiation or limit rule, keep all chain factors, and check exceptional points.
✅ Step-by-Step Solution
Final Answer: \(\frac{\operatorname{asin}{\left(x^{4} \right)}}{4}\) + C.
- Work on each open interval where the original integrand is real and defined.
- u=x⁴, du=4x³dx.
- An antiderivative is F(x)=\(\frac{\operatorname{asin}{\left(x^{4} \right)}}{4}\).
- Differentiate this expression to check that F′(x)=\(\frac{x^{3}}{\sqrt{1 - x^{8}}}\). Add an arbitrary constant C on each domain component.
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