Pertanyaan

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

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

N. Mustikowati

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Pembahasan

Misal :

$U equals 3 x to the power of 2 space end exponent plus space 2 x d u space equals space left parenthesis 6 x plus 2 right parenthesis d x d x equals fraction numerator 1 over denominator 6 x space plus 2 end fraction d u equals fraction numerator 1 over denominator 2 left parenthesis 3 x plus 1 right parenthesis end fraction d u equals integral left parenthesis space 3 x space plus space 1 right parenthesis. left parenthesis 3 x squared space plus space 2 x space right parenthesis to the power of 1 half end exponent space d x equals integral left parenthesis space 3 x space plus space 1 right parenthesis. U to the power of 1 half end exponent fraction numerator 1 over denominator 2 left parenthesis 3 x plus 1 right parenthesis end fraction d u equals integral 1 half U to the power of 1 half end exponent plus c equals 1 half.2 over 3 U to the power of 3 over 2 end exponent plus c equals 1 third U square root of U plus c equals 1 third left parenthesis space 3 x squared space plus space 2 x right parenthesis square root of 3 x squared space plus 2 x end root plus c$