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Problem Evaluate ∫ x 3 + 2 x 2 + 3 x + 5 x 2 + 1 d x \displaystyle \int \frac{x^{3}+2x^{2}+3x+5}{x^{2}+1}\,dx ∫ x 2 + 1 x 3 + 2 x 2 + 3 x + 5 d x x 2 2 + 2 x + 1 2 ln ( x 2 + 1 ) + 3 arctan x + C \displaystyle \frac{x^{2}}{2}+2x+\tfrac12\ln\!\big(x^{2}+1\big)+3\arctan x+C 2 x 2 + 2 x + 2 1 ln ( x 2 + 1 ) + 3 arctan x + C x 2 2 + 2 x + ln ( x 2 + 1 ) + 3 arctan x + C \displaystyle \frac{x^{2}}{2}+2x+\ln\!\big(x^{2}+1\big)+3\arctan x+C 2 x 2 + 2 x + ln ( x 2 + 1 ) + 3 arctan x + C x 2 + 2 x + ln ( x 2 + 1 ) + 3 arctan x + C \displaystyle x^{2}+2x+\ln\!\big(x^{2}+1\big)+3\arctan x+C x 2 + 2 x + ln ( x 2 + 1 ) + 3 arctan x + C x 2 2 + 2 x + ln ( x 2 + 1 ) + arctan x + C \displaystyle \frac{x^{2}}{2}+2x+\ln\!\big(x^{2}+1\big)+\arctan x+C 2 x 2 + 2 x + ln ( x 2 + 1 ) + arctan x + C Browse the problem library