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Problem Determine ∫ 3 x 2 + 5 x + 2 x 3 + x d x \displaystyle \int \frac{3x^{2}+5x+2}{x^{3}+x}\,dx ∫ x 3 + x 3 x 2 + 5 x + 2 d x 2 ln ∣ x ∣ + ln ( x 2 + 1 ) + 5 arctan x + C 2\ln|x|+\ln(x^{2}+1)+5\arctan x + C 2 ln ∣ x ∣ + ln ( x 2 + 1 ) + 5 arctan x + C ln ∣ x ∣ + 1 2 ln ( x 2 + 1 ) + 5 arctan x + C \ln|x|+\dfrac{1}{2}\ln(x^{2}+1)+5\arctan x + C ln ∣ x ∣ + 2 1 ln ( x 2 + 1 ) + 5 arctan x + C 2 ln ∣ x ∣ + 1 2 ln ( x 2 + 1 ) + 5 arctan x + C 2\ln|x|+\dfrac{1}{2}\ln(x^{2}+1)+5\arctan x + C 2 ln ∣ x ∣ + 2 1 ln ( x 2 + 1 ) + 5 arctan x + C 2 ln ∣ x ∣ + 1 2 ln ( x 2 + 1 ) + 5 2 arctan x + C 2\ln|x|+\dfrac{1}{2}\ln(x^{2}+1)+\dfrac{5}{2}\arctan x + C 2 ln ∣ x ∣ + 2 1 ln ( x 2 + 1 ) + 2 5 arctan x + C Browse the problem library