Ejerccicios De Integracion Por Partes.docx

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EJERCCICIOS DE INTEGRACION POR PARTES

โˆซ ๐‘ฅ๐‘ ๐‘’๐‘›๐‘ฅ๐‘‘๐‘ฅ

1. Hallar la integral:

Soluciรณn: ๐‘ข=๐‘ฅ ๐‘‘๐‘ข = ๐‘‘๐‘ฅ โˆซ ๐‘ฅ๐‘ ๐‘’๐‘›๐‘ฅ๐‘‘๐‘ฅ = {๐‘‘๐‘ฃ = ๐‘ ๐‘’๐‘›๐‘ฅ๐‘‘๐‘ฅ { ๐‘ฃ = ๐‘๐‘œ๐‘ ๐‘ฅ = โˆ’๐‘ฅ๐‘๐‘œ๐‘ ๐‘ฅ + โˆซ ๐‘๐‘œ๐‘ ๐‘ฅ๐‘‘๐‘ฅ = โˆ’๐‘ฅ๐‘๐‘œ๐‘ ๐‘ฅ + ๐‘ ๐‘’๐‘›๐‘ฅ + ๐‘

2. Hallar el integral:

โˆซ ๐‘ฅ 3 โˆš1 + ๐‘ฅ 2 ๐‘‘๐‘ฅ

๐‘ข = ๐‘ฅ2 { ๐‘‘๐‘ฃ = ๐‘ฅโˆš1 + ๐‘ฅ 2 ๐‘‘๐‘ฅ

๐‘‘๐‘ข = 2๐‘ฅ๐‘‘๐‘ฅ

3 { โˆš1+๐‘ฅ 2 2๐‘ฅ๐‘‘๐‘ฅ (1+๐‘ฅ 2 ) โ„2 ๐‘ฃ = โˆซ ๐‘ฅโˆš1 + ๐‘ฅ 2 ๐‘‘๐‘ฅ = โˆซ = = 2 2.3โ„2

โˆซ ๐‘ฅ 3 โˆš1 + ๐‘ฅ 2 ๐‘‘ = 1 (1+๐‘ฅ 2 )5โ„2 3

5โ„2

=

1 3

๐‘ฅ 2 (1+๐‘ฅ 2 )3โ„2 3

1 3

1

(1 + ๐‘ฅ 2 )3โ„2

โˆ’ โˆซ(1 + ๐‘ฅ 2 )3โ„2 2๐‘ฅ๐‘‘๐‘ฅ = 3

๐‘ฅ 2 (1 + ๐‘ฅ 2 )3โ„2 โˆ’

2 15

(1 + ๐‘ฅ 2 )5โ„2 + ๐‘

๐‘ฅ 2 (1+๐‘ฅ 2 )3โ„2 3

โˆ’

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