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Model Paper 1 — Applied Maths STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceApplied MathsModel Paper 11 Mark
MCQ
$\int \frac{(\log x)^5}{x}$ is equal to
  • A
    $\frac{\log x^6}{6}+C$
  • B
    $\frac{(\log x)^6}{3 x^2}+C$
  • ✓
    $\frac{(\log x)^6}{6}+C$
  • D
    $\frac{\log x^6}{3 x^2}+C$
✓

Answer

Correct option: C.
$\frac{(\log x)^6}{6}+C$
(c) $\frac{(\log x)^6}{6}+C$
Explanation
Put $\log x = t \Rightarrow \frac{1}{x} dx = dt$
$
\therefore \int \frac{(\log x)^5}{x} d x=\int t^5 d t=\frac{t^6}{6}+C=\frac{(\log x)^6}{6}+C
$

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