Find ∫ x + 7 ( x + 8 ) 5 d xI tried ∫ x + 7 ( x + 8 ) 5 d x but I couldn’t complete it. Is there any simpler way to integrate this?

Question

Find  ∫            x      +      7              (      x      +      8              )        5                 d  xI tried   ∫            x      +      7              (      x      +      8              )        5                 d  x but I couldn’t complete it. Is there any simpler way to integrate this?

Grace Moses · Accepted Answer

Try u-substitution.Let   u  =  x  +  8 (or   u  −  1  =  x  +  7), then   d  u  =  (  x  +  8      )    ′    d  x  =  d  x and so we have  ∫            x      +      7              (      x      +      8              )        5                d  x  =  ∫            u      −      1              u      5          d  u  =  ∫      1          u      4          d  u  −  ∫      1          u      5          d  uUse power rule to solve these integrals and don&#039;t forget to substitute   x  +  8 back into u when done

pobi1k · Accepted Answer

∫            x      +      7              (      x      +      8              )        5              d  xUpon the substitution   u  =  x  +  8 ,   d  u  =  d  x, we get  ∫            u      −      1              u      5        d  u  =  ∫            u              −        4              −            u              −        5              d  u  =            u              −        3                    −      3        +            u              −        4              4    +  C  =            (      x      +      8              )                  −          3                            −      3        +            (      x      +      8              )                  −          4                      4    +  C  .

Find int (x+7)/((x+8)^5) dx but I couldn’t complete it. Is there any simpler way to integrate this?

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