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Hasil dari begin mathsize 14px style integral open parentheses negative 19 over x cubed minus 5 x to the power of 5 square root of x minus fraction numerator 4 square root of x over denominator x to the power of 5 end fraction close parentheses blank d x end style adalah ....

  1. begin mathsize 14px style fraction numerator 19 over denominator 2 x squared end fraction plus 10 over 13 x to the power of 6 square root of x plus fraction numerator 8 over denominator 7 x cubed square root of x end fraction plus C end style 

  2. begin mathsize 14px style fraction numerator 19 over denominator 2 x squared end fraction minus 10 over 13 x to the power of 6 square root of x plus fraction numerator 8 over denominator 7 x cubed square root of x end fraction plus C end style 

  3. begin mathsize 14px style fraction numerator 19 over denominator 2 x squared end fraction minus 10 over 13 x to the power of 6 square root of x minus fraction numerator 8 over denominator 7 x cubed square root of x end fraction plus C end style 

  4. begin mathsize 14px style fraction numerator 57 over denominator 2 x squared end fraction minus 25 over 13 x to the power of 6 square root of x plus fraction numerator 8 over denominator 7 x cubed square root of x end fraction plus C end style 

  5. begin mathsize 14px style negative fraction numerator 57 over denominator 2 x squared end fraction plus 25 over 13 x to the power of 6 square root of x plus fraction numerator 8 over denominator 7 x cubed square root of x end fraction plus C end style 

R. RGFLSATU

Master Teacher

Jawaban terverifikasi

Pembahasan

Perhatikan perhitungan berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral open parentheses negative 19 over x cubed minus 5 x to the power of 5 square root of x minus fraction numerator 4 square root of x over denominator x to the power of 5 end fraction close parentheses blank d x end cell equals cell integral negative 19 over x cubed blank d x minus integral 5 x to the power of 5 square root of x blank d x minus integral fraction numerator 4 square root of x over denominator x to the power of 5 end fraction blank d x end cell row blank equals cell integral negative 19 x to the power of negative 3 end exponent blank d x minus integral 5 x to the power of 11 over 2 end exponent blank d x minus integral 4 x to the power of negative 9 over 2 end exponent blank d x end cell row blank equals cell open parentheses fraction numerator negative 19 over denominator negative 3 plus 1 end fraction x to the power of negative 3 plus 1 end exponent plus C subscript 1 close parentheses minus open parentheses fraction numerator 5 over denominator 11 over 2 plus 1 end fraction x to the power of 11 over 2 plus 1 end exponent plus C subscript 2 close parentheses minus open parentheses fraction numerator 4 over denominator negative 9 over 2 plus 1 end fraction x to the power of negative 9 over 2 plus 1 end exponent plus C subscript 3 close parentheses end cell row blank equals cell fraction numerator negative 19 over denominator negative 2 end fraction x to the power of negative 2 end exponent plus C subscript 1 minus fraction numerator 5 over denominator 13 over 2 end fraction x to the power of 13 over 2 end exponent minus C subscript 2 minus fraction numerator 4 over denominator negative 7 over 2 end fraction x to the power of negative 7 over 2 end exponent minus C subscript 3 end cell row blank equals cell 19 over 2 times 1 over x squared plus C subscript 1 minus 5 times 2 over 13 x to the power of 13 over 2 end exponent minus C subscript 2 minus 4 times open parentheses negative 2 over 7 close parentheses times 1 over x to the power of 7 over 2 end exponent blank minus C subscript 3 end cell row blank equals cell fraction numerator 19 over denominator 2 x squared end fraction minus 10 over 13 x to the power of 6 plus 1 half end exponent plus fraction numerator 8 over denominator 7 x cubed square root of x end fraction plus C subscript 1 minus C subscript 2 minus C subscript 3 end cell row blank equals cell fraction numerator 19 over denominator 2 x squared end fraction minus 10 over 13 x to the power of 6 times x to the power of 1 half end exponent plus fraction numerator 8 over denominator 7 x cubed square root of x end fraction plus C subscript 1 minus C subscript 2 minus C subscript 3 end cell row blank equals cell fraction numerator 19 over denominator 2 x squared end fraction minus 10 over 13 x to the power of 6 square root of x plus fraction numerator 8 over denominator 7 x cubed square root of x end fraction plus C subscript 1 minus C subscript 2 minus C subscript 3 end cell end table end style  

Misalkan begin mathsize 14px style C subscript 1 minus C subscript 2 minus C subscript 3 equals C comma end style maka

begin mathsize 14px style fraction numerator 19 over denominator 2 x squared end fraction minus 10 over 13 x to the power of 6 square root of x plus fraction numerator 8 over denominator 7 x cubed square root of x end fraction plus C subscript 1 minus C subscript 2 minus C subscript 3 equals fraction numerator 19 over denominator 2 x squared end fraction minus 10 over 13 x to the power of 6 square root of x plus fraction numerator 8 over denominator 7 x cubed square root of x end fraction plus C end style 

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