Pertanyaan

Hasil dari ∫ x 3 − 3 x + 2 ( x + 1 ) ( x − 1 ) d x = …

Hasil dari $\int \frac{( x + 1 ) ( x - 1 )}{x ^{3} - 3 x + 2} d x = \dots$

M. Mariyam

Master Teacher

Mahasiswa/Alumni Institut Pertanian Bogor

Jawaban terverifikasi

Pembahasan

Jadi, jawaban yang tepat adalah D.

$integral fraction numerator size 14px left parenthesis size 14px x size 14px plus size 14px 1 size 14px right parenthesis size 14px left parenthesis size 14px x size 14px minus size 14px 1 size 14px right parenthesis over denominator square root of size 14px x to the power of size 14px 3 size 14px minus size 14px 3 size 14px x size 14px plus size 14px 2 end root end fraction d x equals integral fraction numerator x squared minus 1 over denominator square root of size 14px x to the power of size 14px 3 size 14px minus size 14px 3 size 14px x size 14px plus size 14px 2 end root end fraction d x misal space colon u equals size 14px x to the power of size 14px 3 size 14px minus size 14px 3 size 14px x size 14px plus size 14px 2 size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space fraction numerator size 14px d size 14px u over denominator size 14px d size 14px x end fraction size 14px equals size 14px 3 size 14px x to the power of size 14px 2 size 14px minus size 14px 3 size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px 1 over size 14px 3 size 14px d size 14px u size 14px equals begin mathsize 14px style left parenthesis x squared minus 1 right parenthesis end style size 14px d size 14px x$

$begin mathsize 14px style integral fraction numerator x squared minus 1 over denominator square root of x cubed minus 3 x plus 2 end root end fraction d x equals integral fraction numerator 1 over denominator 3 square root of u end fraction d u space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 1 third integral u to the power of negative 1 half end exponent d u space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 1 third times 2 u to the power of 1 half end exponent plus C space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 2 over 3 square root of x cubed minus 3 x plus 2 end root plus C end style$

Jadi, jawaban yang tepat adalah D.