Pertanyaan

Hasil dari ∫ x ( x + 4 ) 7 d x = … + 3 m u .

Hasil dari $\int x (x + 4)^{7} d x = \dots + 3 m u .$

A. Acfreelance

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban soal ini terdapat pada pilihan (D)

Pembahasan

Diberikan bentuk integral . Karena terdiri dari perkalian dua fungsi maka dapat dimisalkan Maka dengan metode substitusi, diperoleh: Jadi, jawaban soal ini terdapat pada pilihan (D)

Diberikan bentuk integral integral x left parenthesis x plus 4 right parenthesis to the power of 7 straight d x . Karena terdiri dari perkalian dua fungsi maka dapat dimisalkan

table attributes columnalign right center left columnspacing 0px end attributes row u equals cell x plus 4 end cell row x equals cell u minus 4 end cell row cell straight d x end cell equals cell straight d u end cell end table

Maka dengan metode substitusi, diperoleh:

$table attributes columnalign right center left columnspacing 0px end attributes row cell integral x left parenthesis x plus 4 right parenthesis to the power of 7 straight d x end cell equals cell integral open parentheses u minus 4 close parentheses u to the power of 7 d u end cell row blank equals cell integral open parentheses u times u to the power of 7 minus 4 u to the power of 7 close parentheses d u end cell row blank equals cell integral open parentheses u to the power of 8 minus 4 u to the power of 7 close parentheses d u end cell row blank equals cell 1 over 9 u to the power of 9 minus 4 over 8 u to the power of 8 plus C end cell row blank equals cell 1 over 9 open parentheses x plus 4 close parentheses to the power of 9 minus 1 half open parentheses x plus 4 close parentheses to the power of 8 plus C end cell row blank equals cell open parentheses x plus 4 close parentheses to the power of 8 open parentheses 1 over 9 open parentheses x plus 4 close parentheses minus 1 half close parentheses plus C end cell row blank equals cell open parentheses x plus 4 close parentheses to the power of 8 open parentheses 1 over 9 x plus 4 over 9 minus 1 half close parentheses plus C end cell row blank equals cell open parentheses x plus 4 close parentheses to the power of 8 open parentheses 1 over 9 x plus 8 over 18 minus 9 over 18 close parentheses plus C end cell row blank equals cell open parentheses x plus 4 close parentheses to the power of 8 open parentheses 1 over 9 x minus 1 over 18 close parentheses plus C end cell row blank equals cell 1 over 9 open parentheses x plus 4 close parentheses to the power of 8 open parentheses x minus 1 half close parentheses plus C end cell row blank equals cell 1 over 9 open parentheses x plus 4 close parentheses to the power of 8 open parentheses fraction numerator 2 x minus 1 over denominator 2 end fraction close parentheses plus C end cell row blank equals cell 1 over 18 left parenthesis 2 x minus 1 right parenthesis open parentheses x plus 4 close parentheses to the power of 8 plus C end cell end table$

Jadi, jawaban soal ini terdapat pada pilihan (D)