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Hasil dari ∫ x 2 − 4 x + 10 ​ 3 x − 6 ​ d x adalah....

Hasil dari  adalah.... 

  1. begin mathsize 14px style 3 square root of x squared minus 4 x plus 10 end root plus C end style 

  2. begin mathsize 14px style 2 square root of x squared minus 4 x plus 10 end root plus C end style 

  3. begin mathsize 14px style 1 third square root of x squared minus 4 x plus 10 end root plus C end style  

  4. size 14px 2 over size 14px 3 square root of size 14px x to the power of size 14px 2 size 14px minus size 14px 4 size 14px x size 14px plus size 14px 10 end root size 14px plus size 14px C 

  5. begin mathsize 14px style 3 over 2 square root of x squared minus 4 x plus 10 end root plus C end style 12

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Y. Endah

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

jawaban yang tepat adalah A.

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Pembahasan

Misalkan , maka sehingga Jadi, jawaban yang tepat adalah A.

Misalkan begin mathsize 14px style u equals x squared minus 4 x plus 10 end style, maka begin mathsize 14px style fraction numerator d u over denominator d x end fraction equals 2 x minus 4 space atau space fraction numerator d u over denominator 2 x minus 4 end fraction equals d x end style sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral fraction numerator 3 x minus 6 over denominator square root of x squared minus 4 x plus 10 end root end fraction d x end cell equals cell integral fraction numerator 3 x minus 6 over denominator open parentheses x squared minus 4 x plus 10 close parentheses to the power of begin display style 1 half end style end exponent end fraction d x end cell row blank equals cell integral fraction numerator 3 open parentheses x minus 2 close parentheses over denominator u to the power of begin display style 1 half end style end exponent end fraction times fraction numerator d u over denominator 2 open parentheses x minus 2 close parentheses end fraction end cell row blank equals cell integral 3 over 2 fraction numerator d u over denominator u to the power of 1 half end exponent end fraction end cell row blank equals cell 3 over 2 integral u to the power of negative 1 half end exponent d u end cell row blank equals cell 3 over 2 times 2 space u to the power of 1 half end exponent plus C end cell row blank equals cell 3 u to the power of 1 half end exponent plus C end cell row blank equals cell 3 square root of x squared minus 4 x plus 10 end root plus C end cell end table end style

Jadi, jawaban yang tepat adalah A.

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