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∫ ( x 7 1 ​ + x 2 ) d x = ....

 

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P. Afrisno

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

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diperoleh .

diperoleh 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 1 over x to the power of 7 plus x squared close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table 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 table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 1 over denominator 6 x to the power of 6 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell x cubed over 3 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank C end table.

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Pembahasan

Jika diberikan fungsi maka dapat ditentukan integral tak tentu dari fungsi tersebut sebagai berikut. Sehingga dapat ditentukan hasil dari sebagai berikut. Jadi, diperoleh .

Jika diberikan fungsi f open parentheses x close parentheses equals a x to the power of n plus b x to the power of m maka dapat ditentukan integral tak tentu dari fungsi tersebut sebagai berikut.

integral open parentheses a x to the power of n plus b x to the power of m close parentheses space d x equals fraction numerator a over denominator n plus 1 end fraction x to the power of n plus 1 end exponent plus fraction numerator b over denominator m plus 1 end fraction x to the power of m plus 1 end exponent plus C 

Sehingga dapat ditentukan hasil dari integral open parentheses 1 over x to the power of 7 plus x squared close parentheses space d x sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell integral open parentheses 1 over x to the power of 7 plus x squared close parentheses space d x end cell equals cell integral open parentheses x to the power of negative 7 end exponent plus x squared close parentheses space d x end cell row blank equals cell fraction numerator 1 over denominator negative 7 plus 1 end fraction x to the power of negative 7 plus 1 end exponent plus fraction numerator 1 over denominator 2 plus 1 end fraction x to the power of 2 plus 1 end exponent plus C end cell row blank equals cell fraction numerator 1 over denominator negative 6 end fraction x to the power of negative 6 end exponent plus 1 third x cubed plus C end cell row blank equals cell negative fraction numerator 1 over denominator 6 x to the power of 6 end fraction plus x cubed over 3 plus C end cell end table 

Jadi, diperoleh 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 1 over x to the power of 7 plus x squared close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table 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 table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 1 over denominator 6 x to the power of 6 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell x cubed over 3 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank C end table.

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