Class 12 Integrals · Conceptual Answer1 Marksindefinite_integration
Class 12 Maths · Integrals · Conceptual Answer #43
Evaluate \(\int x^{4} \log{\left(x \right)}\,dx\). Work for x>0.
✅ Step-by-Step Solution
Final Answer: \(\frac{x^{5} \log{\left(x \right)}}{5} - \frac{x^{5}}{25}\) + C
- Use parts with u=ln x,dv=x⁴dx: I=x⁵ln x/5−(1/5)∫x⁴dx=x⁵ln x/5−x⁵/25+C.
- Therefore the required integral is \(\frac{x^{5} \log{\left(x \right)}}{5} - \frac{x^{5}}{25}\) + C.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Use parts with u=ln x,dv=x⁴dx: I=x⁵ln x/5−(1/5)∫x⁴dx=x⁵ln x/5−x⁵/25+C.
- [0.5 marks] Therefore the required integral is \(\frac{x^{5} \log{\left(x \right)}}{5} - \frac{x^{5}}{25}\) + C.
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