Pertanyaan

Hasil dari ∫ 3 x 2 + 9 x − 1 2 x + 3 d x = ...

Hasil dari $\int \frac{2 x + 3}{3 x ^{2} + 9 x - 1} d x = ...$

Y. Herlanda

Master Teacher

Mahasiswa/Alumni STKIP PGRI Jombang

Jawaban terverifikasi

Jawaban

hasil integral di atas adalah .

hasil integral di atas adalah

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 2 over 3 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 3 x squared plus 9 x minus 1 end root end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank C end table

Pembahasan

Misal: Maka: Jadi, hasil integral di atas adalah .

$integral fraction numerator 2 x plus 3 over denominator square root of 3 x squared plus 9 x minus 1 end root end fraction d x equals integral open parentheses 2 x plus 3 close parentheses open parentheses 3 x squared plus 9 x minus 1 close parentheses to the power of negative 1 half end exponent space d x$

Misal:

$table attributes columnalign right center left columnspacing 0px end attributes row u equals cell 3 x squared plus 9 x minus 1 end cell row cell fraction numerator d u over denominator d x end fraction end cell equals cell 6 x plus 9 end cell row cell d u end cell equals cell 6 x plus 9 space d x end cell end table$

Maka:

$table attributes columnalign right center left columnspacing 0px end attributes row cell integral open parentheses 2 x plus 3 close parentheses times u to the power of negative 1 half end exponent space d x end cell equals cell integral u to the power of negative 1 half end exponent space times open parentheses 2 x plus 3 close parentheses d x end cell row blank equals cell integral u to the power of negative 1 half end exponent space times 1 third open parentheses 6 x plus 9 close parentheses d x end cell row blank equals cell integral u to the power of negative 1 half end exponent space times 1 third d u end cell row blank equals cell 1 third times fraction numerator 1 over denominator negative begin display style 1 half end style plus 1 end fraction u to the power of negative 1 half plus 1 end exponent plus C end cell row blank equals cell 1 third times fraction numerator 1 over denominator begin display style 1 half end style end fraction u to the power of 1 half end exponent plus C end cell row blank equals cell 1 third times 2 u to the power of 1 half end exponent plus C end cell row blank equals cell 2 over 3 square root of u plus C end cell row blank equals cell 2 over 3 square root of 3 x squared plus 9 x minus 1 end root plus C end cell end table$

Jadi, hasil integral di atas adalah .