Antiderivative of 8 t − 1 / 2 I am trying to find the antiderivative of 8 t − 1 / 2 but im just not understanding how to do this.I saw someone get out of t 1 / 2 the answer 2 t 1 / 2 . Can someone help me out?

Question

Antiderivative of   8      t          −              1                  /                2            I am trying to find the antiderivative of   8      t          −              1                  /                2             but im just not understanding how to do this.I saw someone get out of       t          1              /            2       the answer   2      t          1              /            2      . Can someone help me out?

Trey Ross · Accepted Answer

Step 1Don&#039;t be worried about a negative exponent that&#039;s not -1: you apply the same rules as you would when integrating, say,           ∫    8          t      3        d    t    ,      , for example.Those rules, recall, are:Step 2For any   n  ≠  −  1 and any number b,  ∫  b  ⋅      x    n    d  x    =    b  ∫      x    n    d  x    =    b  ⋅      1          (      n      +      1      )            x          (      n      +      1      )        +  C        (where           C         is a constant)    .  So, since      (  −  1      /    2  )  ≠  −  1  ,    ∫  8      t          −      1              /            2        d  t  =      8          (              1        2            )            t                (      −              1        2            )            +            1      )        +  C    =    …    ?

Sonia Gay · Accepted Answer

Explanation:  ∫      x    α    d  x  =      1          α      +      1            x          α      +      1        +  C, as long as   α  ≠  −  1. Also, note that   ∫  8      t          −              1        2              d  t  =  8  ∫      t          −              1        2              d  t.

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