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Integrals

Question
CBSEENMA12036229
Wired Faculty App

integral space open curly brackets fraction numerator left parenthesis log space straight x minus 1 right parenthesis over denominator 1 plus left parenthesis log space straight x right parenthesis squared end fraction close curly brackets squared space dx space is space equal space to
  • fraction numerator log space straight x over denominator left parenthesis log space straight x right parenthesis squared plus 1 end fraction plus space straight C
  • fraction numerator straight x over denominator straight x plus 1 end fraction space plus straight C
  • fraction numerator xe to the power of straight x over denominator 1 plus straight x squared end fraction plus straight C
  • fraction numerator straight x over denominator left parenthesis log space straight x right parenthesis squared space plus space 1 end fraction plus space straight C

Solution

D.

fraction numerator straight x over denominator left parenthesis log space straight x right parenthesis squared space plus space 1 end fraction plus space straight C integral fraction numerator left parenthesis log space straight x minus 1 right parenthesis squared over denominator left parenthesis 1 plus left parenthesis log space straight x right parenthesis squared right parenthesis squared end fraction dx space equals space integral space open square brackets fraction numerator 1 over denominator left parenthesis 1 plus left parenthesis log space straight x right parenthesis squared right parenthesis end fraction minus fraction numerator 2 space log space straight x over denominator left parenthesis 1 plus left parenthesis log space straight x right parenthesis squared right parenthesis squared end fraction close square brackets space dx space equals integral open square brackets fraction numerator straight e to the power of straight t over denominator 1 plus straight t squared end fraction minus fraction numerator 2 straight t space straight e to the power of straight t over denominator left parenthesis 1 plus straight t squared right parenthesis squared end fraction close square brackets space dt space put space log space straight x space equals space straight t rightwards double arrow space dx space equals straight e to the power of straight t space dt integral straight e to the power of straight t space open square brackets fraction numerator 1 over denominator 1 plus straight t squared end fraction minus fraction numerator 2 straight t over denominator left parenthesis 1 plus straight t squared right parenthesis squared end fraction close square brackets dt space equals space fraction numerator straight e to the power of straight t over denominator 1 plus straight t squared end fraction space plus straight c equals space fraction numerator straight x over denominator 1 plus space left parenthesis log space straight x right parenthesis squared end fraction space plus straight c

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