Pertanyaan

Integral dari 5 x 2 ( x 3 − 2 ) 7 adalah ...

Integral dari $5 x^{2} (x^{3} - 2)^{7}$ adalah ...

H. Eka

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

Error converting from MathML to accessible text.

Pembahasan

Ingat aturan integral berikut. Pada soal tersebut, penyelesaian integral menggunakan metode integral substitusi. Misal: sehingga diperoleh hubungan berikut. Selanjutnya, perhatikan perhitungan berikut ini. Ingat bahwa sehingga diperoleh Dengan demikian,

Ingat aturan integral berikut.

$integral a x to the power of n space text d end text x equals fraction numerator a over denominator n plus 1 end fraction x to the power of n plus 1 end exponent plus c$

Pada soal tersebut, penyelesaian integral menggunakan metode integral substitusi.

integral 5 x squared open parentheses x cubed minus 2 close parentheses to the power of 7 text d end text x

Misal: u equals x cubed minus 2 sehingga diperoleh hubungan berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator text d end text u over denominator text d end text x end fraction end cell equals cell 3 x squared end cell row cell integral open parentheses fraction numerator text d end text u over denominator text d end text x end fraction close parentheses text d end text x end cell equals cell integral 3 x squared space text d end text x end cell row cell integral text d end text u end cell equals cell integral 3 x squared space text d end text x end cell row cell integral fraction numerator 1 over denominator 3 x squared end fraction text d end text u end cell equals cell integral text d end text x end cell end table$

Selanjutnya, perhatikan perhitungan berikut ini.

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell integral 5 x squared open parentheses x cubed minus 2 close parentheses to the power of 7 space text d end text x end cell row blank equals cell integral 5 x squared times u to the power of 7 times fraction numerator 1 over denominator 3 x squared end fraction text d end text u end cell row blank equals cell integral 5 over 3 u to the power of 7 space text d end text u end cell row blank equals cell 5 over 3 times 1 over 8 u to the power of 8 plus C end cell row blank equals cell 5 over 24 u to the power of 8 plus C end cell end table$

Ingat bahwa u equals x cubed minus 2 sehingga diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell integral 5 x squared open parentheses x cubed minus 2 close parentheses to the power of 7 space text d end text x end cell equals cell 5 over 24 u to the power of 8 plus C end cell row blank equals cell 5 over 24 open parentheses x cubed minus 2 close parentheses to the power of 8 plus C end cell end table

Dengan demikian, Error converting from MathML to accessible text.