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begin mathsize 14px style integral space fraction numerator 4 over denominator cube root of 6 x minus 5 end root end fraction space d x equals... end style 

  1. begin mathsize 14px style 5 cube root of open parentheses 6 x minus 5 close parentheses squared end root plus C end style 

  2. begin mathsize 14px style 4 cube root of open parentheses 6 x minus 5 close parentheses squared end root plus C end style 

  3. begin mathsize 14px style 3 cube root of open parentheses 6 x minus 5 close parentheses squared end root plus C end style 

  4. begin mathsize 14px style 2 cube root of open parentheses 6 x minus 5 close parentheses squared end root plus C end style 

  5. begin mathsize 14px style cube root of open parentheses 6 x minus 5 close parentheses squared end root plus C end style 

Jawaban:

Misalkan:

begin mathsize 14px style 6 x minus 5 equals u end style 

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 6 row cell d x end cell equals cell 1 over 6 d u end cell end table end style 

Dengan menerapkan penyelesaian integral dengan metode substitusi, diperoleh perhitungan sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral space fraction numerator 4 over denominator cube root of 6 x minus 5 end root end fraction space d x end cell equals cell integral space fraction numerator 4 over denominator cube root of u end fraction space 1 over 6 d u end cell row blank equals cell integral space 2 over 3 u to the power of negative 1 third end exponent space d u end cell row blank equals cell 2 over 3 times fraction numerator 1 over denominator negative begin display style 1 third end style plus 1 end fraction u to the power of negative 1 third plus 1 end exponent plus C end cell row blank equals cell up diagonal strike 2 over 3 end strike times fraction numerator 1 over denominator begin display style up diagonal strike 2 over 3 end strike end style end fraction u to the power of 2 over 3 end exponent plus C end cell row blank equals cell u to the power of 2 over 3 end exponent plus C end cell row blank equals cell open parentheses 6 x minus 5 close parentheses to the power of 2 over 3 end exponent plus C end cell row blank equals cell cube root of open parentheses 6 x minus 5 close parentheses squared end root plus C end cell end table end style 

Jadi, hasil dari begin mathsize 14px style integral space fraction numerator 4 over denominator cube root of 6 x minus 5 end root end fraction space d x end style adalah begin mathsize 14px style cube root of open parentheses 6 x minus 5 close parentheses squared end root plus C end style.

Dengan demikian, jawaban yang tepat adalah E.

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