Question

Sederhanakan bentuknya lalu operasikan soal berikut
[tex]\displaystyle \int \frac{x^4+x^2+1}{x^2-x+1}~dx[/tex]

Answer 1

Verified answer

Jawaban:

[tex] \frac{1}{3} {x}^{3} + \frac{ 1 }{2} {x}^{2} + x + C[/tex]

Penjelasan dengan langkah-langkah:

[tex]\displaystyle \int \frac{x^4+x^2+1}{x^2-x+1}~dx[/tex]

[tex] \displaystyle = \int \frac{( {x}^{2} + x + 1 )( {x}^{2} - x + 1)}{x^2-x+1}~dx[/tex]

[tex] = \displaystyle \int \frac{( {x}^{2} + x + 1 ) \cancel{( {x}^{2} - x + 1)}}{ \cancel{(x^2-x+1)}}~dx[/tex]

[tex] = \displaystyle \int {x}^{2} + x + 1 \: ~dx[/tex]

[tex] = ( {\frac{1}{2 + 1} x}^{2 + 1}) + ( \frac{1}{1 + 1} {x}^{1 + 1}) + (x) + C[/tex]

[tex] = \frac{1}{3} {x}^{3} + \frac{ 1 }{2} {x}^{2} + x + C[/tex]