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

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

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

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

  4. begin mathsize 14px style 2 space 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:

Menentukan nilai begin mathsize 14px style integral fraction numerator 4 over denominator cube root of 6 x minus 5 end root end fraction d x end style dengan integral subtitusi.

Misal:

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Sehingga soal dapat ditulis sebagai berikut:

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

Dengan demikian, diperoleh begin mathsize 14px style integral fraction numerator 4 over denominator cube root of 6 x minus 5 end root end fraction d x equals cube root of left parenthesis 6 x minus 5 right parenthesis squared end root plus straight C end style.

Jadi, jawaban yang tepat adalah E.

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