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Kelli100500
@Kelli100500
August 2021
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x^4 dx / x^2 +1
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Vas61
Т.к. степень числителя больше степени знаменателя, то нужно разделить числитель на знаменатель
x⁴/(x²+1)=x²-1+1/(x²+1)
∫x⁴dx/(x²+1)=∫(x²-1+1/(x²+1))dx=∫x²dx-∫dx+∫dx/(x²+1)=x³/3-x+arctgx+C
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Answers & Comments
x⁴/(x²+1)=x²-1+1/(x²+1)
∫x⁴dx/(x²+1)=∫(x²-1+1/(x²+1))dx=∫x²dx-∫dx+∫dx/(x²+1)=x³/3-x+arctgx+C