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Hasil dari $begin mathsize 14px style integral open parentheses fraction numerator 3 t squared minus square root of t over denominator 4 t end fraction close parentheses open parentheses 3 minus open parentheses fraction numerator t over denominator 2 square root of t end fraction minus square root of t close parentheses open parentheses 1 over t squared close parentheses close parentheses blank d t end style$ adalah ...

$begin mathsize 14px style 2 open parentheses fraction numerator 3 t squared minus square root of t over denominator 4 t end fraction close parentheses squared plus C end style$
$begin mathsize 14px style 2 open parentheses fraction numerator 3 t squared minus square root of t over denominator 2 t end fraction close parentheses squared plus C end style$
$begin mathsize 14px style 4 open parentheses fraction numerator 3 t squared minus square root of t over denominator 4 t end fraction close parentheses squared plus C end style$
$begin mathsize 14px style 4 open parentheses fraction numerator 3 t squared minus square root of t over denominator 2 t end fraction close parentheses squared plus C end style$
$begin mathsize 14px style 4 open parentheses fraction numerator 3 t squared minus square root of t over denominator 4 t end fraction close parentheses plus C end style$

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$begin mathsize 14px style integral open parentheses fraction numerator 3 t squared minus square root of t over denominator 4 t end fraction close parentheses open parentheses 3 minus open parentheses fraction numerator t over denominator 2 square root of t end fraction times 1 over t squared minus fraction numerator square root of t over denominator t squared end fraction close parentheses close parentheses blank d t equals integral open parentheses fraction numerator 3 t squared minus square root of t over denominator 4 t end fraction close parentheses open parentheses 3 minus open parentheses fraction numerator 1 over denominator 2 t square root of t end fraction minus fraction numerator square root of t over denominator t squared end fraction close parentheses close parentheses blank d t equals integral open parentheses fraction numerator 3 t squared minus square root of t over denominator 4 t end fraction close parentheses open parentheses 3 minus open parentheses t to the power of negative 3 over 2 end exponent over 2 minus t to the power of negative 3 over 2 end exponent close parentheses close parentheses blank d t equals integral open parentheses fraction numerator 3 t squared minus square root of t over denominator 4 t end fraction close parentheses open parentheses 3 minus open parentheses 1 half minus 1 close parentheses t to the power of negative 3 over 2 end exponent close parentheses blank d t equals integral open parentheses fraction numerator 3 t squared minus square root of t over denominator 4 t end fraction close parentheses open parentheses 3 minus open parentheses negative 1 half close parentheses t to the power of negative 3 over 2 end exponent close parentheses blank d t end style$

Dimisalkan $begin mathsize 14px style fraction numerator 3 t squared minus square root of t over denominator 4 t end fraction equals u. end style$ Perhatikan bahwa

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 3 t squared minus square root of t over denominator 4 t end fraction end cell equals u row cell 1 fourth open parentheses 3 t minus fraction numerator square root of t over denominator t end fraction close parentheses end cell equals u row cell 1 fourth open parentheses 3 t minus t to the power of negative 1 half end exponent close parentheses end cell equals u row cell 1 fourth open parentheses 3 minus open parentheses negative 1 half close parentheses t to the power of negative 3 over 2 end exponent close parentheses end cell equals cell fraction numerator d u over denominator d t end fraction end cell row cell integral 1 fourth open parentheses 3 minus open parentheses negative 1 half close parentheses t to the power of negative 3 over 2 end exponent close parentheses d t end cell equals cell integral fraction numerator d u over denominator d t end fraction d t end cell row cell integral 1 fourth open parentheses 3 minus open parentheses negative 1 half close parentheses t to the power of negative 3 over 2 end exponent close parentheses d t end cell equals cell integral d u end cell end table end style$

Maka kita peroleh

$begin mathsize 14px style integral open parentheses fraction numerator 3 t squared minus square root of t over denominator 4 t end fraction close parentheses open parentheses 3 minus open parentheses negative 1 half close parentheses t to the power of negative 3 over 2 end exponent close parentheses blank d t equals integral 4 times 1 fourth times open parentheses fraction numerator 3 t squared minus square root of t over denominator 4 t end fraction close parentheses open parentheses 3 minus open parentheses negative 1 half close parentheses t to the power of negative 3 over 2 end exponent close parentheses blank d t equals integral 4 open parentheses fraction numerator 3 t squared minus square root of t over denominator 4 t end fraction close parentheses 1 fourth open parentheses 3 minus open parentheses negative 1 half close parentheses t to the power of negative 3 over 2 end exponent close parentheses blank d t equals 4 integral u d u equals 4 times 1 half times u squared plus C equals 2 u squared plus C equals 2 open parentheses fraction numerator 3 t squared minus square root of t over denominator 4 t end fraction close parentheses squared plus C end style$