Pertanyaan

Selesaikanlah integral berikut! e. ∫ x 2 x 2 − 3 d x

Selesaikanlah integral berikut!

e. $\int \frac{x ^{2} - 3}{x ^{2}} d x$

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Habis dalam

Klaim

R. Septa

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

.

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank integral end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator x squared minus 3 over denominator x squared end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight d end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 3 over x end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank C end table$ .

Pembahasan

Perhatikan perhitungan berikut. Jadi, .

Perhatikan perhitungan berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row cell integral fraction numerator x squared minus 3 over denominator x squared end fraction space straight d x end cell equals cell integral x to the power of negative 2 end exponent open parentheses x squared minus 3 close parentheses space straight d x end cell row blank equals cell integral 1 minus 3 x to the power of negative 2 end exponent space straight d x end cell row blank equals cell x minus fraction numerator 3 over denominator negative 1 end fraction x to the power of negative 1 end exponent plus C end cell row blank equals cell x plus 3 x to the power of negative 1 end exponent plus C end cell row blank equals cell x plus 3 over x plus C end cell end table$

Jadi, $table attributes columnalign right center left columnspacing 0px end attributes row blank blank integral end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator x squared minus 3 over denominator x squared end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight d end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 3 over x end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank C end table$ .