Pertanyaan

∫ x 1 + x d x adalah....

$\int x 1 + x d x$ adalah....

$fraction numerator 2 x over denominator 3 end fraction left parenthesis 1 plus x right parenthesis to the power of 3 over 2 end exponent minus 4 over 15 left parenthesis 1 plus x right parenthesis to the power of 5 over 2 end exponent plus C$
$fraction numerator 2 x over denominator 3 end fraction left parenthesis 1 plus x right parenthesis to the power of 3 over 2 end exponent minus 1 over 15 left parenthesis 1 plus x right parenthesis to the power of 5 over 2 end exponent plus C$
$fraction numerator 2 x over denominator 3 end fraction left parenthesis 1 plus x right parenthesis to the power of 3 over 2 end exponent minus 4 over 3 left parenthesis 1 plus x right parenthesis to the power of 5 over 2 end exponent plus C$
$fraction numerator 2 x over denominator 3 end fraction left parenthesis 1 plus x right parenthesis to the power of 3 over 2 end exponent minus 5 over 7 left parenthesis 1 plus x right parenthesis to the power of 5 over 2 end exponent plus C$

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Jawaban terverifikasi

Pembahasan

Pilih u=x, sehingga du=dx abaikan C (tambahkan C padaakhir prosesintegral)

Pilih u=x, sehingga du=dx

d v equals square root of 1 plus x end root space d x comma space v equals integral square root of 1 plus x space end root d x integral left parenthesis 1 plus x right parenthesis to the power of 1 half end exponent space d x v equals 2 over 3 left parenthesis 1 plus x right parenthesis to the power of 3 over 2 end exponent space

abaikan C (tambahkan C pada akhir proses integral)

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral u space d v end cell equals cell u v minus integral v space d u space diperoleh end cell row blank equals cell x space.2 over 3 left parenthesis 1 plus x right parenthesis to the power of 3 over 2 end exponent minus integral 2 over 3 left parenthesis 1 plus x right parenthesis to the power of 3 over 2 end exponent d x end cell row blank equals cell fraction numerator 2 x over denominator 3 end fraction left parenthesis 1 plus x right parenthesis to the power of 3 over 2 end exponent minus 2 over 3.2 over 5 left parenthesis 1 plus x right parenthesis to the power of 5 over 2 end exponent plus C end cell row blank equals cell fraction numerator 2 x over denominator 3 end fraction left parenthesis 1 plus x right parenthesis to the power of 3 over 2 end exponent minus 4 over 15 left parenthesis 1 plus x right parenthesis to the power of 5 over 2 end exponent plus C end cell end table end style$