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Tentukan hasil integral tentu fungsi-fungsi berikut! 5. ∫ 2 3 ( 3 x − 2 ) ( 3 x + 4 ) d x

Tentukan hasil integral tentu fungsi-fungsi berikut!

5. $\int_{2}^{3} (3 x - 2) (3 x + 4) d x$

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$begin mathsize 14px style integral subscript 2 superscript 3 open parentheses 3 x minus 2 close parentheses open parentheses 3 x plus 4 close parentheses d x equals integral subscript 2 superscript 3 9 x squared plus 6 x minus 8 space d x space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals integral subscript 2 superscript 3 9 x squared space d x plus integral subscript 2 superscript 3 6 x space d x minus integral subscript 2 superscript 3 8 space d x space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals right enclose fraction numerator 9 over denominator 2 plus 1 end fraction x to the power of 2 plus 1 end exponent end enclose subscript 2 superscript 3 plus right enclose fraction numerator 6 over denominator 1 plus 1 end fraction x to the power of 1 plus 1 end exponent end enclose subscript 2 superscript 3 minus right enclose fraction numerator 8 over denominator 0 plus 1 end fraction x to the power of 0 plus 1 end exponent end enclose subscript 2 superscript 3 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals right enclose 3 x cubed end enclose subscript 2 superscript 3 plus right enclose 3 x squared end enclose subscript 2 superscript 3 minus right enclose 8 x end enclose subscript 2 superscript 3 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals open parentheses 3 left parenthesis 3 right parenthesis cubed minus 3 left parenthesis 2 right parenthesis cubed close parentheses plus open parentheses 3 left parenthesis 3 right parenthesis squared minus 3 left parenthesis 2 right parenthesis squared close parentheses minus open parentheses 8 left parenthesis 3 right parenthesis minus 8 left parenthesis 2 right parenthesis close parentheses space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 57 plus 15 minus 8 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 64 end style$