Use a table of integrals to evaluate the following indefinite integrals. Some of the integrals require preliminary work, such as completing the square or changing variables, before they be found in a table. ∫ ln 2 ⁡ x d x

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Use a table of integrals to evaluate the following indefinite integrals. Some of the integrals require preliminary work, such as completing the square or changing variables, before they be found in a table.   ∫      ln          2        ⁡  x  d  x

dwubiegrw · Accepted Answer

Given:  ∫      ln          2        ⁡  (  x  )  d  xUsing Integration by parts  ∫      ln          2        ⁡  (  x  )  d  x  =      ln          2        ⁡  (  x  )  ∫  1  d  x  −  ∫  (      d          d      x        (      ln          2        ⁡  (  x  )  )  ∫  1  d  x  )  d  x  ∫      ln          2        ⁡  (  x  )  d  x  =  x      ln          2        ⁡  (  x  )  −  ∫  2  ln  ⁡  (  x  )  d  x  ∫      ln          2        ⁡  (  x  )  d  x  =  x      ln          2        ⁡  (  x  )  −  2  ∫  ln  ⁡  (  x  )  d  x  ∫      ln          2        ⁡  (  x  )  d  x  =  x      ln          2        ⁡  (  x  )  −  2  (  x  ln  ⁡  (  x  )  −  x  )  ∫      ln          2        ⁡  (  x  )  d  x  =  x      ln          2        ⁡  (  x  )  −  2  x  ln  ⁡  (  x  )  +  2  x  +  CWhere C is a constant.Result:  ∫      ln          2        ⁡  (  x  )  d  x  =  x      ln          2        ⁡  (  x  )  −  2  x  ln  ⁡  (  x  )  +  2  x  +  CWhere C is a constant.

Use a table of integrals to evaluate the following indefinite integrals. Some of the integrals require preliminary work, such as completing the square or changing variables, before they be found in a table. int ln^(2)xdx

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