Pertanyaan

Hasil dari ∫ ( x 3 4 + 2 x 2 − x 2 3 ) d x = …

Hasil dari $\int (\frac{4}{x ^{3}} + 2 x^{2} - \frac{3}{x ^{2}}) d x = \dots$

$2 over x to the power of 4 plus fraction numerator 2 x cubed over denominator 3 end fraction minus 1 over x cubed plus C$
$1 over x to the power of 4 plus fraction numerator 2 x cubed over denominator 3 end fraction minus 1 over x cubed plus C$
$negative 2 over x squared plus fraction numerator 2 x cubed over denominator 3 end fraction plus 3 over x plus C$
$2 over x to the power of 4 plus fraction numerator 2 x cubed over denominator 3 end fraction minus 2 over x cubed plus C$
$2 over x to the power of 5 plus fraction numerator 2 x cubed over denominator 3 end fraction minus 3 over x cubed plus C$

L. Sibuea

Master Teacher

Mahasiswa/Alumni Universitas Riau

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

Misalkan: Dengan menggunakan sifat integral tak tentu, maka akan diperoleh: Oleh karena itu, jawaban yang benar adalah C.

Misalkan:
f left parenthesis x right parenthesis equals open parentheses 4 over x cubed plus 2 x squared minus 3 over x squared close parentheses

Dengan menggunakan sifat integral tak tentu, maka akan diperoleh:

$table attributes columnalign right center left columnspacing 0px end attributes row cell integral f left parenthesis x right parenthesis d x end cell equals cell integral 4 over x cubed d x plus integral 2 x squared d x minus integral 3 over x squared d x end cell row blank equals cell 4 times integral 1 over x cubed d x plus 2 times integral x squared d x minus 3 times integral 1 over x squared d x end cell row blank equals cell 4 times integral x to the power of negative 3 end exponent d x plus 2 times x cubed over 3 minus 3 times integral x to the power of negative 2 end exponent d x end cell row blank equals cell 4 times fraction numerator x to the power of negative 2 end exponent over denominator negative 2 end fraction plus fraction numerator 2 x cubed over denominator 3 end fraction minus 3 times fraction numerator x to the power of negative 1 end exponent over denominator negative 1 end fraction plus C end cell row cell integral f left parenthesis x right parenthesis d x end cell equals cell negative 2 over x squared plus fraction numerator 2 x cubed over denominator 3 end fraction plus 3 over x plus C end cell end table$

Oleh karena itu, jawaban yang benar adalah C.