Pertanyaan

∫ x 3 − 27 6 x 2 dx

$\int \frac{6 x ^{2} dx}{x ^{3} - 27}$

R. RGFLLIMA

Master Teacher

Jawaban terverifikasi

Jawaban

i,

i, $integral fraction numerator 6 straight x squared dx over denominator square root of straight x cubed minus 27 end root end fraction equals 4 square root of straight x cubed minus 27 end root plus straight C$

Pembahasan

Dengan menerapkan konsep integral substitusi . Misalkan: Maka: Jadii,

Dengan menerapkan konsep integral substitusi .

$integral fraction numerator 6 straight x squared dx over denominator square root of straight x cubed minus 27 end root end fraction$

Misalkan:

$table attributes columnalign right center left columnspacing 0px end attributes row straight u equals cell straight x cubed minus 27 end cell row cell du over dx end cell equals cell 3 straight x squared end cell row dx equals cell fraction numerator du over denominator 3 straight x squared end fraction end cell end table$

Maka:

$table attributes columnalign right center left columnspacing 0px end attributes row cell integral fraction numerator 6 straight x squared dx over denominator square root of straight x cubed minus 27 end root end fraction end cell equals cell integral fraction numerator 6 straight x squared begin display style fraction numerator du over denominator 3 straight x squared end fraction end style over denominator square root of straight U end fraction end cell row blank equals cell integral fraction numerator 2 space du over denominator square root of straight U end fraction end cell row blank equals cell 2 integral 1 over straight U to the power of begin display style 1 half end style end exponent end cell row blank equals cell 2 integral straight U to the power of negative 1 half end exponent end cell row blank equals cell 2 times fraction numerator straight U to the power of negative begin display style 1 half end style plus 1 end exponent over denominator negative begin display style 1 half end style plus 1 end fraction plus straight C end cell row blank equals cell 2 times fraction numerator straight U to the power of begin display style 1 half end style end exponent over denominator begin display style 1 half end style end fraction plus straight C end cell row blank equals cell 2 times square root of straight U times 2 plus straight C end cell row blank equals cell 4 square root of straight U plus straight C end cell row blank equals cell 4 square root of straight x cubed minus 27 end root plus straight C end cell end table$

Jadii, $integral fraction numerator 6 straight x squared dx over denominator square root of straight x cubed minus 27 end root end fraction equals 4 square root of straight x cubed minus 27 end root plus straight C$