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Carilah ∫ x 2 − 1 3 ​ d x !

Carilah !

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L. Sibuea

Master Teacher

Mahasiswa/Alumni Universitas Riau

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nilai dari adalah

nilai dari integral fraction numerator 3 over denominator x squared minus 1 end fraction d x adalah 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 3 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 1 half ln space open vertical bar x plus 1 close vertical bar minus 1 half ln space open vertical bar x minus 1 close vertical bar close parentheses 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 table attributes columnalign right center left columnspacing 0px end attributes row blank blank. end table 

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Pembahasan

Dengan menggunakan sifat integral, maka diperoleh: Dengan demikian, nilai dari adalah

Dengan menggunakan sifat integral, maka diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell integral fraction numerator 3 over denominator x squared minus 1 end fraction d x end cell equals cell 3 times open parentheses integral fraction numerator 1 over denominator x squared minus 1 end fraction d x close parentheses end cell row blank equals cell 3 times open parentheses integral fraction numerator 1 over denominator negative left parenthesis negative x squared plus 1 right parenthesis end fraction d x close parentheses end cell row blank equals cell 3 times open parentheses negative integral fraction numerator 1 over denominator negative x squared plus 1 end fraction d x close parentheses end cell row blank equals cell 3 times open parentheses negative open parentheses fraction numerator ln space open vertical bar x plus 1 close vertical bar over denominator 2 end fraction close parentheses minus fraction numerator ln space open vertical bar x minus 1 close vertical bar over denominator 2 end fraction close parentheses plus C end cell row cell integral fraction numerator 3 over denominator x squared minus 1 end fraction d x end cell equals cell negative 3 open parentheses 1 half ln space open vertical bar x plus 1 close vertical bar minus 1 half ln space open vertical bar x minus 1 close vertical bar close parentheses plus C end cell end table 

Dengan demikian, nilai dari integral fraction numerator 3 over denominator x squared minus 1 end fraction d x adalah 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 3 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 1 half ln space open vertical bar x plus 1 close vertical bar minus 1 half ln space open vertical bar x minus 1 close vertical bar close parentheses 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 table attributes columnalign right center left columnspacing 0px end attributes row blank blank. end table 

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