Pertanyaan

Hasil dari adalah ....

Hasil dari $begin mathsize 14px style integral fraction numerator open parentheses 5 x plus 15 close parentheses squared over denominator left parenthesis x plus 3 right parenthesis end fraction blank d x end style$ adalah ....

$begin mathsize 14px style fraction numerator 5 x squared over denominator 2 end fraction plus 75 x plus C end style$
$begin mathsize 14px style fraction numerator 25 x squared over denominator 2 end fraction plus 75 x plus C end style$

H. Nufus

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Perhatikan perhitungan berikut. Misalkan maka Jadi, jawaban yang tepat adalah D.

Perhatikan perhitungan berikut.

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral fraction numerator open parentheses 5 x plus 15 close parentheses squared over denominator left parenthesis x plus 3 right parenthesis end fraction blank d x end cell equals cell integral fraction numerator open parentheses 5 x plus 15 close parentheses open parentheses 5 x plus 15 close parentheses over denominator x plus 3 end fraction blank d x end cell row blank equals cell integral fraction numerator open parentheses 5 open parentheses x plus 3 close parentheses close parentheses open parentheses 5 open parentheses x plus 3 close parentheses close parentheses over denominator x plus 3 end fraction blank d x end cell row blank equals cell integral fraction numerator 25 open parentheses x plus 3 close parentheses open parentheses x plus 3 close parentheses over denominator x plus 3 end fraction blank d x end cell row blank equals cell integral 25 open parentheses x plus 3 close parentheses blank d x end cell row blank equals cell 25 open parentheses integral x blank d x plus integral 3 blank d x close parentheses end cell row blank equals cell 25 open parentheses open parentheses fraction numerator 1 over denominator 1 plus 1 end fraction x to the power of 1 plus 1 end exponent plus C subscript 1 close parentheses plus open parentheses 3 x plus C subscript 2 close parentheses close parentheses end cell row blank equals cell 25 open parentheses x squared over 2 plus 3 x plus C subscript 1 plus C subscript 2 close parentheses end cell row blank equals cell fraction numerator 25 x squared over denominator 2 end fraction plus 75 x plus 25 C subscript 1 plus 25 C subscript 2 end cell end table end style$

Misalkan maka

$begin mathsize 14px style fraction numerator 25 x squared over denominator 2 end fraction plus 75 x plus 25 C subscript 1 plus 25 C subscript 2 equals fraction numerator 25 x squared over denominator 2 end fraction plus 75 x plus C end style$

Jadi, jawaban yang tepat adalah D.