Find the integral: ∫ 7 x + 9 d x

Question

Find the integral:  ∫      7    x    +    9    d  x

Milton Gilmore · Accepted Answer

Use Power Substitution.Let   u  =      7    x    +    9    ,  x  =                    u                  2                    −      9        7    , and   d  x  =            2      u        7    d  uSubstitute variables from above.  ∫  u  ×            2      u        7    d  uUse Constant Factor Rule:   ∫  c  f  (  x  )  d  x  =  c  ∫  f  (  x  )  d  x  .      2    7    ∫      u          2        d  uUse Power Rule:   ∫      x          n        d  x  =            x              n        +        1                    n      +      1        +  C            2              u                  3                      21  Substitute   u  =      7    x    +    9   back into the original integral.            2                        7          x          +          9                          3                      21  Add constant.            2      (      7      x      +      9              )                              3            2                                21    +  C

Find the integral: int sqrt(7x+9) dx

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Answer & Explanation

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