0∫ x^4 / ( x² + 1 ) dx
As the degree of numerator is higher than that of the denominator, let's divide x^4 by ( x² + 1 ).
= ∫ x² - 1 + 1/(x² + 1 ) dx
= ∫ x² dx - ∫1•dx + 1/ ( 1 + x² ) dx
= [ ( x³ / 3 ) - ( x ) + tan‾1 ( x ) + C ]
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As the degree of numerator is higher than that of the denominator, let's divide x^4 by ( x² + 1 ).
= ∫ x² - 1 + 1/(x² + 1 ) dx
= ∫ x² dx - ∫1•dx + 1/ ( 1 + x² ) dx
= [ ( x³ / 3 ) - ( x ) + tan‾1 ( x ) + C ]
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