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Integralkan setiap bentuk berikut terhadap variabel x. x32​+x23​+5

Pertanyaan

Integralkan setiap bentuk berikut terhadap variabel x.

begin mathsize 14px style 2 over x cubed plus 3 over x squared plus 5 end style  

S. Nur

Master Teacher

Jawaban terverifikasi

Jawaban

integral dari begin mathsize 14px style 2 over x cubed plus 3 over x squared plus 5 end style terhadap variabel x adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell negative 1 over x squared minus 3 over x plus 5 x plus C end cell end table.

Pembahasan

Ingat bagaimana cara mengintegralkan suatu fungsi dengan integral tak tentu yaitu

integral a x to the power of n d x equals fraction numerator a over denominator n plus 1 end fraction x to the power of n plus 1 end exponent plus C 

dan ingat sifat dari integral berikut.

 integral open parentheses f left parenthesis x right parenthesis plus g left parenthesis x right parenthesis close parentheses space d x equals integral f left parenthesis x right parenthesis space d x plus integral g left parenthesis x right parenthesis space d x

Dari rumus di atas, maka diperoleh:

integral open parentheses 2 over x cubed plus 3 over x squared plus 5 close parentheses space straight d x equals integral 2 over x cubed straight d x space plus integral 3 over x squared straight d x plus integral 5 space straight d x equals integral 2 x to the power of negative 3 end exponent straight d x space plus integral 3 x to the power of negative 2 end exponent straight d x plus integral 5 space straight d x equals fraction numerator 2 over denominator negative 3 plus 1 end fraction x to the power of negative 3 plus 1 end exponent space plus C plus fraction numerator 3 over denominator negative 2 plus 1 end fraction x to the power of negative 2 plus 1 end exponent plus C plus 5 over 1 x to the power of 0 plus 1 end exponent plus C equals fraction numerator 2 over denominator negative 2 end fraction x to the power of negative 2 end exponent plus fraction numerator 3 over denominator negative 1 end fraction x to the power of negative 1 end exponent plus 5 over 1 x plus C equals negative x to the power of negative 2 end exponent minus 3 x to the power of negative 1 end exponent plus 5 x plus C equals negative 1 over x squared minus 3 over x plus 5 x plus C


Dengan demikian, integral dari begin mathsize 14px style 2 over x cubed plus 3 over x squared plus 5 end style terhadap variabel x adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell negative 1 over x squared minus 3 over x plus 5 x plus C end cell end table.

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