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∫ x ( x + 4 ) 5 dx = ...

 

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S. Amamah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

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Pembahasan

Misalkan: Sehingga:

Misalkan:

  begin mathsize 14px style u equals x plus 4 rightwards arrow d u equals d x x equals u minus 4 end style 

Sehingga:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral x open parentheses x plus 4 close parentheses to the power of 5 dx end cell equals cell integral open parentheses straight u minus 4 close parentheses straight u to the power of 5 space du end cell row blank equals cell integral straight u to the power of 6 minus 4 straight u to the power of 5 space du end cell row blank equals cell 1 over 7 straight u to the power of 7 minus 4 over 6 straight u to the power of 6 plus C end cell row blank equals cell 1 over 7 open parentheses straight x plus 4 close parentheses to the power of 7 minus 2 over 3 open parentheses straight x plus 4 close parentheses to the power of 6 plus C end cell row blank equals cell 1 over 21 open parentheses x plus 4 close parentheses to the power of 6 open square brackets 3 open parentheses x plus 4 close parentheses minus 14 close square brackets plus C end cell row blank equals cell 1 over 21 open parentheses x plus 4 close parentheses to the power of 6 open parentheses 3 x plus 12 minus 14 close parentheses plus C end cell row blank equals cell 1 over 21 open parentheses 3 x minus 2 close parentheses open parentheses x plus 4 close parentheses to the power of 6 plus C end cell row blank blank blank end table end style

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