Pertanyaan

Hasil dari ....

Ikuti Tryout SNBT & Menangkan E-Wallet 100rb

Habis dalam

Klaim

N. Rahayu

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Pembahasan

Misalkan: u = cot ⁡6x Maka, Sehingga integral di atas menjadi,

Misalkan:
u = cot ⁡6x

Maka,

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator d u over denominator d x end fraction end cell equals cell negative 6 csc squared invisible function application 6 x end cell row cell d x end cell equals cell negative fraction numerator d u over denominator 6 csc squared invisible function application 6 x end fraction end cell end table end style$

Sehingga integral di atas menjadi,

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral open parentheses csc invisible function application 6 x close parentheses to the power of 6 d x end cell equals cell integral csc squared invisible function application 6 x open parentheses csc squared invisible function application 6 x close parentheses squared d x end cell row blank equals cell integral csc squared invisible function application 6 x open parentheses 1 plus cot squared invisible function application 6 x close parentheses squared d x end cell row blank equals cell integral csc squared invisible function application 6 x open parentheses 1 plus u squared close parentheses squared times negative fraction numerator d u over denominator 6 csc squared invisible function application 6 x end fraction end cell row blank equals cell negative 1 over 6 integral open parentheses 1 plus u squared close parentheses squared d u end cell row blank equals cell negative 1 over 6 integral open parentheses u to the power of 4 plus 2 u squared plus 1 close parentheses d u end cell row blank equals cell negative 1 over 6 open parentheses 1 fifth u to the power of 5 plus 2 over 3 u cubed plus u close parentheses plus C end cell row blank equals cell negative 1 over 6 open parentheses 1 fifth cot to the power of 5 invisible function application 6 x plus 2 over 3 cot cubed invisible function application 6 x plus cot invisible function application 6 x close parentheses plus C end cell row blank equals cell negative 1 over 6 cot invisible function application 6 x open parentheses 1 fifth cot to the power of 4 invisible function application 6 x plus 2 over 3 cot squared invisible function application 6 x plus 1 close parentheses plus C end cell end table end style$