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Tentukan integral tak tentu berikut ini!

begin mathsize 14px style integral open parentheses x minus 1 over x close parentheses squared d x end style             

P. Tessalonika

Master Teacher

Mahasiswa/Alumni Universitas Negeri Medan

Jawaban terverifikasi

Pembahasan

Ingat bahwa:

integral subscript blank 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 space comma space untuk space n not equal to 1 

Sehingga diperoleh:

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral open parentheses x minus 1 over x close parentheses squared d x end cell equals cell integral open parentheses x squared minus 2 plus 1 over x squared close parentheses d x end cell row blank equals cell integral open parentheses x squared minus 2 plus x to the power of negative 2 end exponent close parentheses d x end cell row blank equals cell fraction numerator 1 over denominator 2 plus 1 end fraction x to the power of 2 plus 1 end exponent minus fraction numerator 2 over denominator 0 plus 1 end fraction x to the power of 0 plus 1 end exponent plus fraction numerator 1 over denominator negative 2 plus 1 end fraction x to the power of negative 2 plus 1 end exponent plus C end cell row blank equals cell 1 third x cubed minus 2 over 1 x to the power of 1 plus fraction numerator 1 over denominator negative 1 end fraction x to the power of negative 1 end exponent plus C end cell row blank equals cell 1 third x cubed minus 2 x minus x to the power of negative 1 end exponent plus C end cell row blank equals cell 1 third x cubed minus 2 x minus 1 over x plus C end cell end table end style 

Dengan demikian, hasil dari begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank integral end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses x minus 1 over x close parentheses end cell end table squared table attributes columnalign right center left columnspacing 0px end attributes row blank blank d end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table end style adalah Error converting from MathML to accessible text..

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