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Nilai dari ∫ − 1 2 x 2 5 x 4 + 4 x 3 + 3 x 2 − 2 d x = ....

Nilai dari $\int_{- 1}^{2} \frac{5 x ^{4} + 4 x ^{3} + 3 x ^{2} - 2}{x ^{2}} d x = ....$

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Pembahasan

Bentuk integral di atas dapat disederhanakan dengan cara pembagian menurun. Karena hasil pembagian bersisa , maka hasil pembagian sisanya = sehingga

Bentuk integral di atas dapat disederhanakan dengan cara pembagian menurun.

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Karena hasil pembagian bersisa , maka hasil pembagian sisanya = sehingga

$integral subscript negative 1 end subscript superscript 2 fraction numerator 5 x to the power of 4 plus 4 x cubed plus 3 x squared minus 2 over denominator x squared end fraction d x equals integral subscript negative 1 end subscript superscript 2 left parenthesis 5 x squared plus 4 x plus 3 minus 2 over x squared right parenthesis d x equals integral subscript negative 1 end subscript superscript 2 left parenthesis 5 x squared plus 4 x plus 3 minus 2 x to the power of negative 2 end exponent right parenthesis d x equals open square brackets fraction numerator 5 over denominator 2 plus 1 end fraction x cubed plus fraction numerator 4 over denominator 1 plus 1 end fraction x squared plus fraction numerator 3 over denominator 0 plus 1 end fraction x to the power of 0 plus 1 end exponent minus fraction numerator 2 over denominator negative 2 plus 1 end fraction x to the power of negative 2 plus 1 end exponent close square brackets subscript negative 1 end subscript superscript 2 equals open square brackets 5 over 3 x cubed plus 4 over 2 x squared plus 3 x minus open parentheses fraction numerator 2 over denominator negative 1 end fraction x to the power of negative 1 end exponent close parentheses close square brackets subscript negative 1 end subscript superscript 2 equals open square brackets 5 over 3 x cubed plus 2 x squared plus 3 x plus 2 over x close square brackets subscript negative 1 end subscript superscript 2 equals open parentheses 5 over 3 left parenthesis 2 right parenthesis cubed plus 2 left parenthesis 2 right parenthesis squared plus 3 left parenthesis 2 right parenthesis plus 2 over 2 close parentheses minus open parentheses 5 over 3 left parenthesis negative 1 right parenthesis cubed plus 2 left parenthesis negative 1 right parenthesis squared plus 3 left parenthesis negative 1 right parenthesis squared plus 3 left parenthesis negative 1 right parenthesis plus fraction numerator 2 over denominator negative 1 end fraction close parentheses equals open parentheses 40 over 3 plus 8 plus 6 plus 1 close parentheses minus open parentheses negative 5 over 3 plus 2 minus 3 minus 2 close parentheses equals 85 over 3 minus open parentheses negative 14 over 3 close parentheses equals 99 over 3 equals 33$