Use a table of integrals to evaluate the following integrals. ∫ x x + 1 d x

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Use a table of integrals to evaluate the following integrals.   ∫      x          x      +      1        d  x

vyhlodatis · Accepted Answer

∫      x          x      +      1        d  xFormula:   ∫            u      d      u              a      +      b      u        =      1          b              2              (  a  +  b  u  −  a  ln  ⁡      |    a  +  b  u      |    )  +  C  u  =  x  ⇒  d  u  =  x, and a=1, b=1Therefore,  ∫      x          x      +      1        d  x  =                              ∫                      x                          1              +              1              x                                d          x                ⏟                    ∫                        u          d          u                          a          +          b          u                      =      1          (      1              )                  2                      (  1  +  1  x  −  1  ln  ⁡      |    1  +  1  x      |    )  +  CSimplify  ∫      x          x      +      1        d  x  =  1  +  x  −  ln  ⁡      |    1  +  x      |    +  C  ∫      x          x      +      1        d  x  =  x  −  ln  ⁡      |    x  +  1      |    +  CResult:  x  −  ln  ⁡      |    x  +  1      |    +  C

Use a table of integrals to evaluate the following integrals. int x/(x+1)dx

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