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$begin mathsize 14px style 2 over 3 x cubed plus 2 over 3 x square root of x plus fraction numerator 1 over denominator 2 x squared end fraction plus C end style$
$begin mathsize 14px style 2 over 3 x cubed minus 2 over 3 x square root of x minus fraction numerator 1 over denominator 2 x squared end fraction plus C end style$
$begin mathsize 14px style 2 over 3 x cubed plus 3 over 2 x square root of x minus fraction numerator 1 over denominator 2 x squared end fraction plus C end style$
$begin mathsize 14px style 2 over 3 x cubed plus 3 over 2 x square root of x plus fraction numerator 1 over denominator 2 x squared end fraction plus C end style$
$begin mathsize 14px style 2 over 3 x cubed plus 2 over 3 x square root of x minus fraction numerator 1 over denominator 2 x squared end fraction plus C end style$

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

Pembahasan

Perhatikan perhitungan berikut! Misalkan maka Jadi, jawaban yang tepat adalah E.

Perhatikan perhitungan berikut!

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral open parentheses 2 x squared plus square root of x plus 1 over x cubed close parentheses d x end cell equals cell integral 2 x squared blank d x plus integral square root of x blank d x plus integral 1 over x cubed blank d x end cell row blank equals cell integral 2 x squared blank d x plus integral x to the power of 1 half end exponent blank d x plus integral x to the power of negative 3 end exponent blank d x end cell row blank equals cell open parentheses fraction numerator 2 over denominator 2 plus 1 end fraction x to the power of 2 plus 1 end exponent plus C subscript 1 close parentheses plus open parentheses fraction numerator 1 over denominator 1 half plus 1 end fraction blank x to the power of 1 half plus 1 end exponent plus C subscript 2 close parentheses plus open parentheses fraction numerator 1 over denominator negative 3 plus 1 end fraction blank x to the power of negative 3 plus 1 end exponent plus C subscript 3 close parentheses end cell row blank equals cell 2 over 3 x cubed plus C subscript 1 plus fraction numerator 1 over denominator 3 over 2 end fraction x to the power of 3 over 2 end exponent plus C subscript 2 plus fraction numerator 1 over denominator negative 2 end fraction x to the power of negative 2 end exponent plus C subscript 3 end cell row blank equals cell 2 over 3 x cubed plus 2 over 3 x square root of x minus 1 half times 1 over x squared plus C subscript 1 plus C subscript 2 plus C subscript 3 end cell row blank equals cell 2 over 3 x cubed plus 2 over 3 x square root of x minus fraction numerator 1 over denominator 2 x squared end fraction plus C subscript 1 plus C subscript 2 plus C subscript 3 end cell end table end style$

Misalkan maka

$begin mathsize 14px style 2 over 3 x cubed plus 2 over 3 x square root of x minus fraction numerator 1 over denominator 2 x squared end fraction plus C subscript 1 plus C subscript 2 plus C subscript 3 equals 2 over 3 x cubed plus 2 over 3 x square root of x minus fraction numerator 1 over denominator 2 x squared end fraction plus C end style$

Jadi, jawaban yang tepat adalah E.