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Class 12 Integrals · Conceptual Answer1 Marksindefinite_integration

Class 12 Maths · Integrals · Conceptual Answer #39

Evaluate \(\int \frac{2 x}{\sqrt[3]{x^{2} + 1}}\,dx\). Work on each connected open interval where the real integrand is defined.

✅ Step-by-Step Solution

Final Answer: \(\frac{3 \left(x^{2} + 1\right)^{\frac{2}{3}}}{2}\) + C
  1. Let u=x²+1, du=2x dx. Then ∫u^(−1/3)du=(3/2)u^(2/3)+C.
  2. Therefore the required integral is \(\frac{3 \left(x^{2} + 1\right)^{\frac{2}{3}}}{2}\) + C.

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] Let u=x²+1, du=2x dx. Then ∫u^(−1/3)du=(3/2)u^(2/3)+C.
  • [0.5 marks] Therefore the required integral is \(\frac{3 \left(x^{2} + 1\right)^{\frac{2}{3}}}{2}\) + C.

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