5
2 2 + 2 + 1 2 , = ln + 2 2 + 2 + 1 = 2 + 2 − 2 2 + 2 + 1 2 + 2 2 + 2 + 1 2 2 + 2 + 1 2 + 2 2 + 2 + 1 → = 2 + 2 + 1 → = 2 + 2 2 + 2 2 + 2 + 1 = = ln + → 2 + 2 + 1 = +1 +1 +1 2 2 + 2 2 + 2 + 1 = ln 2 + 2 + 1 + → 2 + 2 2 + 2 + 1 = ln +1 2 + 2 + 2 2 + 2 + 1 = 2 ln +1 +

Integrales

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Ejemplos de integrales

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  • 2

    2 + 2 + 1

    2 ,

    = ln +

    2

    2 + 2 + 1 =

    2 + 2 2

    2 + 2 + 1

    2 + 2

    2 + 2 + 1

    2

    2 + 2 + 1

    2 + 2

    2 + 2 + 1 = 2 + 2 + 1 = 2 + 2

    2 + 2

    2 + 2 + 1 =

    = ln +

    2 + 2 + 1 = + 1 + 1 + 1 2

    2 + 2

    2 + 2 + 1 = ln 2 + 2 + 1 +

    2 + 2

    2 + 2 + 1 = ln + 1 2 +

    2 + 2

    2 + 2 + 1 = 2 ln + 1 +

  • 2

    2 + 2 + 1 = 2

    1

    2 + 2 + 1

    2 + 2 + 1 = + 1 + 1 + 1 2

    2 1

    2 + 2 + 1 2

    1

    + 1 2 = + 1 =

    2 1

    + 1 2 = 2

    1

    2 2 2 2

    1

    1+ 2

    1

    +

    2 1

    + 1 2 =

    2

    + 1+

    2

    2 + 2 + 1 = 2 ln + 1 +

    2

    + 1+

    2

    2 + 2 + 1 = 2 ln + 1 +

    1

    + 1 +

  • 2 + + 1

    2 + 1

    2 + + 1

    2 + 1 =

    2

    2 + 1 +

    2 + 1 +

    1

    2 + 1

    2

    2 + 1 =

    2 + 1 1

    2 + 1

    2 + 1

    2 + 1

    2 + 1

    1

    2 + 1

    2 + 1 = 2 + 1 = 2 =

    2

    2 + 1

    2

    1

    2

    =1

    2 ln 2 + 1 +

    2

    2 + 1 = arctan +

    2 + 1 =

    1

    2 ln 2 + 1 +

  • 1

    2 + 1 = arctan +

    2 + + 1

    2 + 1 = arctan +

    1

    2 ln 2 + 1 + arctan +

    2 + + 1

    2 + 1 = +

    1

    2 ln 2 + 1 +

  • 1

    ln

    1

    ln =

    1

    ln

    1

    = ln =1

    1

    ln

    1

    =

    1

    = ln +

    1

    ln = ln ln +