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Nilai dari integral subscript 1 superscript 2 fraction numerator 5 x squared over denominator 2 x squared end fraction minus fraction numerator 3 over denominator 2 x squared end fraction space d x equals... space 

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 integral subscript 1 superscript 2 fraction numerator 5 x squared over denominator 2 x squared end fraction minus fraction numerator 3 over denominator 2 x squared end fraction space d x equals 1 3 over 4.

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table attributes columnalign right center left columnspacing 0px end attributes row cell integral subscript a superscript b f open parentheses x close parentheses plus-or-minus g open parentheses x close parentheses space d x end cell equals cell integral subscript a superscript b f open parentheses x close parentheses space d x plus-or-minus integral subscript a superscript b g open parentheses x close parentheses space d x end cell row cell integral subscript a superscript b k f open parentheses x close parentheses space d x end cell equals cell k integral subscript a superscript b f open parentheses x close parentheses space d x end cell end table 

dengan k adalah konstanta.

table attributes columnalign right center left columnspacing 0px end attributes row cell integral subscript 1 superscript 2 fraction numerator 5 x squared over denominator 2 x squared end fraction minus fraction numerator 3 over denominator 2 x squared end fraction space d x end cell equals cell integral subscript 1 superscript 2 fraction numerator 5 x squared over denominator 2 x squared end fraction space d x minus integral subscript 1 superscript 2 fraction numerator 3 over denominator 2 x squared end fraction space d x end cell row cell integral subscript 1 superscript 2 fraction numerator 5 x squared over denominator 2 x squared end fraction minus fraction numerator 3 over denominator 2 x squared end fraction space d x end cell equals cell integral subscript 1 superscript 2 5 over 2 space d x minus 3 over 2 integral subscript 1 superscript 2 x to the power of negative 2 end exponent space d x end cell row cell integral subscript 1 superscript 2 fraction numerator 5 x squared over denominator 2 x squared end fraction minus fraction numerator 3 over denominator 2 x squared end fraction space d x end cell equals cell 5 over 2 open square brackets fraction numerator 1 over denominator 0 plus 1 end fraction x to the power of 0 plus 1 end exponent close square brackets subscript 1 superscript 2 minus 3 over 2 open square brackets fraction numerator 1 over denominator negative 2 plus 1 end fraction x to the power of negative 2 plus 1 end exponent close square brackets subscript 1 superscript 2 end cell row cell integral subscript 1 superscript 2 fraction numerator 5 x squared over denominator 2 x squared end fraction minus fraction numerator 3 over denominator 2 x squared end fraction space d x end cell equals cell 5 over 2 open square brackets x close square brackets subscript 1 superscript 2 minus 3 over 2 open square brackets negative x to the power of negative 1 end exponent close square brackets subscript 1 superscript 2 end cell row cell integral subscript 1 superscript 2 fraction numerator 5 x squared over denominator 2 x squared end fraction minus fraction numerator 3 over denominator 2 x squared end fraction space d x end cell equals cell 5 over 2 open square brackets x close square brackets subscript 1 superscript 2 plus 3 over 2 open square brackets 1 over x close square brackets subscript 1 superscript 2 end cell row cell integral subscript 1 superscript 2 fraction numerator 5 x squared over denominator 2 x squared end fraction minus fraction numerator 3 over denominator 2 x squared end fraction space d x end cell equals cell 5 over 2 left parenthesis 2 minus 1 right parenthesis plus 3 over 2 open parentheses 1 half minus 1 over 1 close parentheses end cell row cell integral subscript 1 superscript 2 fraction numerator 5 x squared over denominator 2 x squared end fraction minus fraction numerator 3 over denominator 2 x squared end fraction space d x end cell equals cell 5 over 2 left parenthesis 1 right parenthesis plus 3 over 2 open parentheses fraction numerator 1 minus 2 over denominator 2 end fraction close parentheses end cell row cell integral subscript 1 superscript 2 fraction numerator 5 x squared over denominator 2 x squared end fraction minus fraction numerator 3 over denominator 2 x squared end fraction space d x end cell equals cell 5 over 2 plus 3 over 2 open parentheses negative 1 half close parentheses end cell row cell integral subscript 1 superscript 2 fraction numerator 5 x squared over denominator 2 x squared end fraction minus fraction numerator 3 over denominator 2 x squared end fraction space d x end cell equals cell 5 over 2 minus 3 over 4 end cell row cell integral subscript 1 superscript 2 fraction numerator 5 x squared over denominator 2 x squared end fraction minus fraction numerator 3 over denominator 2 x squared end fraction space d x end cell equals cell fraction numerator 5 left parenthesis 2 right parenthesis minus 3 over denominator 4 end fraction end cell row cell integral subscript 1 superscript 2 fraction numerator 5 x squared over denominator 2 x squared end fraction minus fraction numerator 3 over denominator 2 x squared end fraction space d x end cell equals cell fraction numerator 10 minus 3 over denominator 4 end fraction end cell row cell integral subscript 1 superscript 2 fraction numerator 5 x squared over denominator 2 x squared end fraction minus fraction numerator 3 over denominator 2 x squared end fraction space d x end cell equals cell 7 over 4 end cell row cell integral subscript 1 superscript 2 fraction numerator 5 x squared over denominator 2 x squared end fraction minus fraction numerator 3 over denominator 2 x squared end fraction space d x end cell equals cell 1 3 over 4 end cell end table 

Jadi, integral subscript 1 superscript 2 fraction numerator 5 x squared over denominator 2 x squared end fraction minus fraction numerator 3 over denominator 2 x squared end fraction space d x equals 1 3 over 4.

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