Pertanyaan

∫ x 2 2 x 3 − 3 x 2 + 1 d x = ...

$\int \frac{2 x ^{3} - 3 x ^{2} + 1}{x ^{2}} d x =$ ...

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

Pembahasan

Operasikan bentuk integral tak tentu tersebut seperti berikut: Maka, Jadi, jawaban yang tepat adalah B.

Operasikan bentuk integral tak tentu tersebut seperti berikut:

$table attributes columnalign right center left columnspacing 0px end attributes row cell integral fraction numerator 2 x cubed minus 3 x squared plus 1 over denominator x squared end fraction d x end cell equals cell integral fraction numerator 2 x cubed over denominator x squared end fraction minus fraction numerator 3 x squared over denominator x squared end fraction plus 1 over x squared d x end cell row blank equals cell integral 2 x minus 3 plus 1 over x squared d x end cell row blank equals cell integral 2 x d x minus integral 3 d x plus integral 1 over x squared d x end cell row blank equals cell integral 2 x d x minus integral 3 d x plus integral x to the power of negative 2 end exponent d x end cell row blank equals cell fraction numerator 2 over denominator 1 plus 1 end fraction x to the power of 1 plus 1 end exponent minus 3 over 1 x to the power of 0 plus 1 end exponent plus fraction numerator 1 over denominator negative 2 plus 1 end fraction x to the power of negative 2 plus 1 end exponent plus C end cell row blank equals cell 2 over 2 x squared minus 3 x to the power of 1 minus x to the power of negative 1 end exponent plus C end cell row blank equals cell x squared minus 3 x minus 1 over x plus C end cell end table$

Maka, $integral fraction numerator 2 x cubed minus 3 x squared plus 1 over denominator x squared end fraction d x equals$ x squared minus 3 x minus 1 over x plus C

Jadi, jawaban yang tepat adalah B.