Pertanyaan

∫ x ( x + 2 ) 5 d x = ...

$\int x (x + 2)^{5} d x = ...$

A. Acfreelance

Master Teacher

Jawaban terverifikasi

Pembahasan

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row u equals cell x rightwards double arrow d u equals d x end cell row cell d v end cell equals cell open parentheses x plus 2 close parentheses to the power of 5 end cell row blank rightwards double arrow cell v equals integral space open parentheses x plus 2 close parentheses to the power of 5 space d x end cell row blank equals cell 1 over 6 open parentheses x plus 2 close parentheses to the power of 6 end cell row blank blank blank row cell integral space u space d v end cell equals cell u v minus integral v space d u end cell row cell integral space x space open parentheses x plus 2 close parentheses to the power of 5 space d x end cell equals cell x open parentheses 1 over 6 open parentheses x plus 2 close parentheses to the power of 6 close parentheses minus integral 1 over 6 open parentheses x plus 2 close parentheses to the power of 6 space d u end cell row blank equals cell 1 over 6 x open parentheses x plus 2 close parentheses to the power of 6 minus integral 1 over 6 open parentheses x plus 2 close parentheses to the power of 6 space d x end cell row blank equals cell 1 over 6 x open parentheses x plus 2 close parentheses to the power of 6 minus 1 over 7 cross times 1 over 6 open parentheses x plus 2 close parentheses to the power of 7 plus c end cell row blank equals cell 1 over 6 open parentheses x plus 2 close parentheses to the power of 6 open square brackets x minus 1 over 7 open parentheses x plus 2 close parentheses close square brackets plus c end cell row blank equals cell 1 over 6 open parentheses x plus 2 close parentheses to the power of 6 open square brackets fraction numerator 7 x over denominator 7 end fraction minus 1 over 7 x plus 2 over 7 close square brackets plus c end cell row blank equals cell 1 over 6 open parentheses fraction numerator 7 x plus 1 over denominator 7 end fraction close parentheses open parentheses x plus 2 close parentheses to the power of 6 plus c end cell row blank equals cell 1 over 42 open parentheses 7 x plus 1 close parentheses open parentheses x plus 2 close parentheses to the power of 6 plus c end cell end table end style$