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Problem Evaluate ∫ 6 x + 1 x 2 + 4 x + 10 d x \displaystyle\int \frac{6x+1}{x^{2}+4x+10}\,dx ∫ x 2 + 4 x + 10 6 x + 1 d x 3 2 ln ∣ x 2 + 4 x + 10 ∣ − 11 6 arctan ( x + 2 6 ) + C \dfrac{3}{2}\ln|x^{2}+4x+10|-\dfrac{11}{\sqrt{6}}\arctan\!\left(\dfrac{x+2}{\sqrt{6}}\right)+C 2 3 ln ∣ x 2 + 4 x + 10∣ − 6 11 arctan ( 6 x + 2 ) + C 3 ln ∣ x 2 + 4 x + 10 ∣ − 11 6 arctan ( x + 2 6 ) + C 3\ln|x^{2}+4x+10|-\dfrac{11}{\sqrt{6}}\arctan\!\left(\dfrac{x+2}{\sqrt{6}}\right)+C 3 ln ∣ x 2 + 4 x + 10∣ − 6 11 arctan ( 6 x + 2 ) + C 3 ln ∣ x 2 + 4 x + 10 ∣ − 11 2 6 arctan ( x + 2 6 ) + C 3\ln|x^{2}+4x+10|-\dfrac{11}{2\sqrt{6}}\arctan\!\left(\dfrac{x+2}{\sqrt{6}}\right)+C 3 ln ∣ x 2 + 4 x + 10∣ − 2 6 11 arctan ( 6 x + 2 ) + C 3 ln ∣ x 2 + 4 x + 10 ∣ + 11 6 arctan ( x + 2 6 ) + C 3\ln|x^{2}+4x+10|+\dfrac{11}{\sqrt{6}}\arctan\!\left(\dfrac{x+2}{\sqrt{6}}\right)+C 3 ln ∣ x 2 + 4 x + 10∣ + 6 11 arctan ( 6 x + 2 ) + C Browse the problem library