The indefinite integral ∫ x 2 1 − x d x

Question

The indefinite integral    ∫      x    2        1    −    x          d    x

toliwask · Accepted Answer

Let   u  =      1    −    x  . Then                     d        u                    d        x              =  −            1              2                  1          −          x                    Thus   d  u  =  −            1              2                  1          −          x                        d  x. You left out the dx, which may be part of the reason you are puzzled.So   d  x  =  −  2      1    −    x      d  u  =  −  2  u    d  uAlso, since       u    2    =  1  −  x, we have   x  =  1  −      u    2  , and therefore       x    2    =  (  1  −      u    2        )    2  Expressing everything in terms of u, we get  ∫  (  1  −      u    2        )    2    (  u  )  (  −  2  u  )    d  u  .

The indefinite integral int x^2 sqrt(1-x)dx

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