Pertanyaan

Tentukan hasil pengintegralan fungsi aljabar berikut. ∫ 3 x 2 − 3 x + 5 4 x − 6 d x

Tentukan hasil pengintegralan fungsi aljabar berikut.

$\int \frac{4 x - 6}{3 x ^{2} - 3 x + 5} d x$

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Klaim

Y. Endah

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

Jawaban terverifikasi

Pembahasan

Misalkan , sehingga

Misalkan $begin mathsize 14px style u equals x squared minus 3 x plus 5 comma space maka space fraction numerator d u over denominator d x end fraction equals 2 x minus 3 space atau space fraction numerator d u over denominator 2 x minus 3 end fraction equals d x end style$ , sehingga

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral fraction numerator 4 x minus 6 over denominator cube root of x squared minus 3 x plus 5 end root end fraction d x end cell equals cell integral fraction numerator 2 open parentheses 2 x minus 3 close parentheses over denominator open parentheses x squared minus 3 x plus 5 close parentheses to the power of begin display style 1 third end style end exponent end fraction d x end cell row blank equals cell integral fraction numerator 2 open parentheses 2 x minus 3 close parentheses over denominator u to the power of begin display style 1 third end style end exponent end fraction times fraction numerator d u over denominator 2 x minus 3 end fraction end cell row blank equals cell 2 integral u to the power of negative 1 third end exponent d u end cell row blank equals cell 2 times 3 over 2 u to the power of 2 over 3 end exponent plus C end cell row blank equals cell 3 cube root of open parentheses x squared minus 3 x plus 5 close parentheses squared end root plus C end cell end table end style$