Help me understand this antiderivativeI have a simple equation I typed into WolframAlpha to see what it was. Look what WO gave me:Indefinite integrals: ∫ 1 2 u d u = u + constant .Possible intermediate steps: ∫ 1 2 u d uFactor out constants: 1 2 ∫ 1 u d uThe integral of 1 u is 2 u : u + constantIs this so? How can the antiderivative of 1 u be 2 u ?

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Help me understand this antiderivativeI have a simple equation I typed into WolframAlpha to see what it was. Look what WO gave me:Indefinite integrals:   ∫      1          2              u              d  u  =      u    +  constant  .Possible intermediate steps:  ∫      1          2              u              d  uFactor out constants:      1    2    ∫      1          u        d  uThe integral of       1          u       is   2      u  :      u    +  constantIs this so? How can the antiderivative of       1          u       be   2      u  ?

Myla Pierce · Accepted Answer

Explanation:Think of       1          u       as       u          −              1        2            . Now you can just apply the power rule (i.e. increase the exponent rule by 1 and divide by the new exponent). This gives                    ∫                  1                      u                                  d        u                            =        ∫                  u                      −                          1              2                                              d        u                                          =                              u                          1              2                                            1            2                          +        C                                          =        2                  u                +        C        .

Help me understand this antiderivative I have a simple equation I typed into WolframAlpha to see wh

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New Questions in Calculus 1