CA Foundation · Quantitative Aptitude · Differential and Integral Calculus
The value of ∫ x²·log x dx is (where C is the constant of integration):
By parts with u = log x and dv = x² dx, the result is (x³/3)log x − ∫x²/3 dx, which equals (x³/3)log x − x³/9 + C.
- A(x³/3) log x − x³/9 + CCorrect
- B(x³/3) log x − x³/3 + C
- C(x³/3) log x + x³/9 + C
- D(x²/2) log x − x²/4 + C
Explanation
Take u = log x and dv = x² dx, so v = x³/3. Then ∫x² log x dx = (x³/3)log x − ∫(x³/3)(1/x)dx = (x³/3)log x − (1/3)(x³/3) = (x³/3)log x − x³/9 + C. Option with x³/3 forgets the extra factor 1/3 from v.
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