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Question Number 20903 by ANTARES_VY last updated on 07/Sep/17

Answered by Joel577 last updated on 07/Sep/17

Using polynomial division,we got I = ∫ x^3 − x^2 + 4x − 4 + ((4x + 1)/(x^2 + x)) dx = ∫ x^3 − x^2 + 4x − 4 dx + ∫ ((4x + 1)/(x^2 + x)) dx P = ∫ ((4x + 1)/(x^2 + x)) dx = ∫ (1/x) + (3/(x + 1)) dx = ln ∣x∣ + 3ln ∣x + 1∣ + C = ln ∣x(x + 1)^3 ∣ + C I = (1/4)x^4 − (1/3)x^3 + 2x^2 − 4x + ln ∣x(x + 1)^3 ∣ + C

Usingpolynomialdivision,wegotI=∫x3−x2+4x−4+4x+1x2+xdx=∫x3−x2+4x−4dx+∫4x+1x2+xdxP=∫4x+1x2+xdx=∫1x+3x+1dx=ln∣x∣+3ln∣x+1∣+C=ln∣x(x+1)3∣+CI=14x4−13x3+2x2−4x+ln∣x(x+1)3∣+C

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