Pertanyaan

Selesaikanlah. ∫ ( x − x 1 ) ( x + x 1 ) ( x 2 − x ) d x

Selesaikanlah.

$\int (x - \frac{1}{x}) (x + \frac{1}{x}) (x^{2} - x) d x$

I. Kumaralalita

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Pembahasan

Untuk memudahkan perhitungan integral, hitung terlebih dahulu hasil perkalian ketiga fungsi diatas. Jadi, hasil dari integral di atas adalah .

Untuk memudahkan perhitungan integral, hitung terlebih dahulu hasil perkalian ketiga fungsi diatas.

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell integral open parentheses open parentheses x minus 1 over x close parentheses open parentheses x plus 1 over x close parentheses close parentheses open parentheses x squared minus x close parentheses space d x end cell row blank equals cell integral open parentheses x squared minus open parentheses 1 over x close parentheses squared close parentheses open parentheses x squared minus x close parentheses space d x end cell row blank equals cell integral open parentheses x squared minus 1 over x squared close parentheses open parentheses x squared minus x close parentheses space d x end cell row blank equals cell integral open parentheses x squared times x squared close parentheses minus open parentheses x squared times x close parentheses minus open parentheses 1 over x squared times x squared close parentheses minus open parentheses 1 over x squared times x close parentheses d x end cell row blank equals cell integral x to the power of 4 minus x cubed minus 1 minus 1 over x space d x end cell row blank equals cell fraction numerator 1 over denominator 4 plus 1 end fraction x to the power of 4 plus 1 end exponent minus fraction numerator 1 over denominator 3 plus 1 end fraction x to the power of 3 plus 1 end exponent minus x to the power of 0 plus 1 end exponent minus ln space x plus C end cell row blank equals cell 1 fifth x to the power of 5 minus 1 fourth x to the power of 4 minus x minus ln space x plus C end cell end table$

Jadi, hasil dari integral di atas adalah

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 fifth x to the power of 5 minus 1 fourth x to the power of 4 minus x minus ln space x plus C end cell end table .