Pertanyaan

Hasil dari ∫ ( x 2 ln 2 x ) dx = … + 3 m u .

Hasil dari $\int (\frac{ln 2 x}{x ^{2}}) dx = \dots + 3 m u .$

$begin mathsize 14px style fraction numerator 1 over denominator 2 straight x end fraction left parenthesis ln left parenthesis 2 straight x right parenthesis plus 1 right parenthesis plus straight C end style$

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N. Rahayu

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Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Pembahasan

Misalkan: dan Maka. Jadi, jawaban yang tepat adalah E.

Misalkan:

begin mathsize 14px style straight u equals ln space left parenthesis 2 straight x right parenthesis du equals 1 half straight x times 2 straight x space dx du equals 1 over straight x dx end style

dan

begin mathsize 14px style dv equals 1 over straight x squared dx integral dv equals integral 1 over straight x squared dx straight v equals negative 1 over straight x dx end style

Maka.

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral fraction numerator ln space 2 straight x over denominator straight x squared end fraction dx end cell equals cell uv minus integral straight v space du end cell row blank equals cell ln left parenthesis 2 straight x right parenthesis times open parentheses negative 1 over straight x close parentheses plus integral 1 over straight x squared du end cell row blank equals cell negative 1 over straight x ln left parenthesis 2 straight x right parenthesis minus 1 over straight x plus straight C end cell row blank equals cell negative 1 over straight x left parenthesis ln left parenthesis 2 straight x right parenthesis plus 1 right parenthesis plus straight C end cell end table end style$

Jadi, jawaban yang tepat adalah E.