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Pertanyaan

integral subscript blank superscript blank fraction numerator 6 x squared over denominator open parentheses 1 plus x cubed close parentheses squared end fraction d x equals   

  1. fraction numerator 1 over denominator 1 plus x cubed end fraction plus straight C  

  2. fraction numerator 2 over denominator 1 plus x cubed end fraction plus straight C 

  3. fraction numerator negative 2 over denominator 1 plus x cubed end fraction plus straight C 

  4. fraction numerator negative 1 over denominator 1 plus x cubed end fraction plus straight C 

  5. fraction numerator 1 over denominator 2 open parentheses 1 plus x cubed close parentheses end fraction plus straight C 

Pembahasan Soal:

Soal diatas dapat diselesaikan dengan menggunakan metode substitusi. Misalkan:

table attributes columnalign right center left columnspacing 0px end attributes row t equals cell 1 plus x cubed end cell row blank rightwards double arrow cell fraction numerator d t over denominator d x end fraction equals 3 x squared end cell row blank rightwards double arrow cell straight d t equals 3 x squared space straight d x end cell end table 

Dengan demikian:

table attributes columnalign right center left columnspacing 0px end attributes row cell integral subscript blank superscript blank fraction numerator 6 x squared over denominator open parentheses 1 plus x cubed close parentheses squared end fraction d x end cell equals cell integral subscript blank superscript blank fraction numerator 2.3 x squared over denominator open parentheses 1 plus x cubed close parentheses squared end fraction d x end cell row blank equals cell integral subscript blank superscript blank 2 over t squared d t end cell row blank equals cell 2 integral subscript blank superscript blank 1 over t squared d t end cell row blank equals cell 2 integral subscript blank superscript blank t to the power of negative 2 end exponent d t end cell row blank equals cell 2 times open parentheses negative t to the power of negative 1 end exponent close parentheses plus straight C end cell row blank equals cell 2 times open parentheses negative 1 over t close parentheses plus straight C end cell row blank equals cell negative 2 over t plus straight C end cell end table 

Substitusi nilai t equals 1 plus x cubed maka:

equals negative 2 over t plus straight C equals negative fraction numerator 2 over denominator 1 plus x cubed end fraction plus straight C 

Oleh karena itu, jawaban yang benar adalah B.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 02 Juni 2021

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