Find the integral: ∫ ln ⁡ x x 5 d x

Question

Find the integral:  ∫            ln      ⁡      x              x              5              d  x

Nigerkamg5 · Accepted Answer

Use Integration by Parts on   ∫            ln      ⁡      x              x              5              d  xLet   u  =  ln  ⁡  x  ,  d  v  =      1          x              5              ,  d  u  =      1    x    d  x  ,  v  =  −      1          4              x                  4                    Substitute the above into   u  v  −  ∫  v  d  u  ..  −            ln      ⁡      x              4              x                  4                      −  ∫  −      1          4              x                  5                      d  xUse Constant Factor Rule:   ∫  c  f  (  x  )  d  x  =  c  ∫  f  (  x  )  d  x  .  −            ln      ⁡      x              4              x                  4                      +      1    4    ∫      1          x              5              d  xUse Power Rule:   ∫      x          n        d  x  =            x              n        +        1                    n      +      1        +  C  −            ln      ⁡      x              4              x                  4                      −      1          16              x                  4                    Add constant.   −            ln      ⁡      x              4              x                  4                      −      1          16              x                  4                      +  C

Find the integral: int ln(x)/x^5 dx

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