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Pertanyaan

Hasil dari begin mathsize 14px style integral fraction numerator open parentheses x plus 1 close parentheses open parentheses x minus 1 close parentheses over denominator square root of x cubed minus 3 x plus 2 end root end fraction d x equals end style...

  1. begin mathsize 14px style 1 over 6 square root of x cubed minus 3 x plus 2 end root plus c end style 

  2. begin mathsize 14px style 1 third square root of x cubed minus 3 x plus 2 end root plus c end style 

  3. begin mathsize 14px style 1 half square root of x cubed minus 3 x plus 2 end root plus c end style 

  4. begin mathsize 14px style 2 over 3 square root of x cubed minus 3 x plus 2 end root plus c end style 

  5. begin mathsize 14px style 3 over 2 square root of x cubed minus 3 x plus 2 end root plus c end style 

Pembahasan Soal:

begin mathsize 14px style integral fraction numerator open parentheses x plus 1 close parentheses open parentheses x minus 1 close parentheses over denominator square root of x cubed minus 3 x plus 2 end root end fraction d x equals end style

begin mathsize 14px style integral fraction numerator open parentheses x squared minus 1 close parentheses over denominator square root of x cubed minus 3 x plus 2 end root end fraction d x end style

Misal: 

begin mathsize 14px style text u=x end text cubed minus 3 x plus 2 fraction numerator d u over denominator d x end fraction equals 3 x squared minus 3 equals 3 open parentheses x squared minus 1 close parentheses d x equals fraction numerator 1 over denominator 3 open parentheses x squared minus 1 close parentheses end fraction d u end style

begin mathsize 14px style integral fraction numerator open parentheses x squared minus 1 close parentheses over denominator square root of x cubed minus 3 x plus 2 end root end fraction d x end style

begin mathsize 14px style equals integral fraction numerator open parentheses x squared minus 1 close parentheses over denominator u to the power of begin display style 1 half end style end exponent end fraction cross times fraction numerator 1 over denominator 3 open parentheses x squared minus 1 close parentheses end fraction d u equals integral open parentheses 1 third cross times 1 over u to the power of begin display style 1 half end style end exponent close parentheses d u equals integral 1 third u to the power of negative 1 half end exponent d u equals 1 third cross times 2 cross times u to the power of 1 half end exponent plus c equals 2 over 3 square root of x cubed minus 3 x plus 2 end root plus c end style

Jadi, jawaban yang tepat adalah D.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 Februari 2021

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