Use a table of integrals to evaluate the following integrals. ∫ x ∗ 2 x 2 d x

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Use a table of integrals to evaluate the following integrals.   ∫  x  ∗      2                  x                  2                      d  x

Gracelyn Paul · Accepted Answer

∫  x  ∗      2                  x                  2                      d  xLet   u  =      x          2        ⇒  d  u  =  2  x  d  x  ⇒  x  d  x  =      1    2    d  uWrite the integral in terms of u  ∫      2                  x                  2                      (  x  )  d  x  =      1    2    ∫      2          u        d  uFormula:   ∫      a          u        d  u  =            a              u                    ln      ⁡      a        +  CTherefore,      1    2    ∫      2          u        d  u  =      1    2    (            2              u                    ln      ⁡      2        )  +  CSimplify            2              u        −        1                    ln      ⁡      2        +  CPutting the answer back in terms of x,   u  =      x          2                  2                        x                      2                          −        1                    ln      ⁡      2        +  C

Use a table of integrals to evaluate the following integrals. int x*2^(x^2)dx

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