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Hasil dari ∫(x34​+2x2−x23​)dx=…

Pertanyaan

Hasil dari integral open parentheses 4 over x cubed plus 2 x squared minus 3 over x squared close parentheses d x equals horizontal ellipsis 

  1. 2 over x to the power of 4 plus fraction numerator 2 x cubed over denominator 3 end fraction minus 1 over x cubed plus C 

  2. 1 over x to the power of 4 plus fraction numerator 2 x cubed over denominator 3 end fraction minus 1 over x cubed plus C 

  3. negative 2 over x squared plus fraction numerator 2 x cubed over denominator 3 end fraction plus 3 over x plus C 

  4. 2 over x to the power of 4 plus fraction numerator 2 x cubed over denominator 3 end fraction minus 2 over x cubed plus C 

  5. 2 over x to the power of 5 plus fraction numerator 2 x cubed over denominator 3 end fraction minus 3 over x cubed plus C 

L. Sibuea

Master Teacher

Mahasiswa/Alumni Universitas Riau

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

Misalkan:
f left parenthesis x right parenthesis equals open parentheses 4 over x cubed plus 2 x squared minus 3 over x squared close parentheses 

Dengan menggunakan sifat integral tak tentu, maka akan diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell integral f left parenthesis x right parenthesis d x end cell equals cell integral 4 over x cubed d x plus integral 2 x squared d x minus integral 3 over x squared d x end cell row blank equals cell 4 times integral 1 over x cubed d x plus 2 times integral x squared d x minus 3 times integral 1 over x squared d x end cell row blank equals cell 4 times integral x to the power of negative 3 end exponent d x plus 2 times x cubed over 3 minus 3 times integral x to the power of negative 2 end exponent d x end cell row blank equals cell 4 times fraction numerator x to the power of negative 2 end exponent over denominator negative 2 end fraction plus fraction numerator 2 x cubed over denominator 3 end fraction minus 3 times fraction numerator x to the power of negative 1 end exponent over denominator negative 1 end fraction plus C end cell row cell integral f left parenthesis x right parenthesis d x end cell equals cell negative 2 over x squared plus fraction numerator 2 x cubed over denominator 3 end fraction plus 3 over x plus C end cell end table  

Oleh karena itu, jawaban yang benar adalah C.

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