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Problem For a nonzero constant a a a ∫ x 2 + a 2 x 2 + 2 a x + a 2 + 1 d x \displaystyle \int \frac{x^{2}+a^{2}}{x^{2}+2ax+a^{2}+1}\,dx ∫ x 2 + 2 a x + a 2 + 1 x 2 + a 2 d x a a a x − a ln ( ( x + a ) 2 + 1 ) + ( 2 a 2 − 1 ) arctan ( x + a ) + C x-a\ln\!\big((x+a)^{2}+1\big)+(2a^{2}-1)\arctan(x+a)+C x − a ln ( ( x + a ) 2 + 1 ) + ( 2 a 2 − 1 ) arctan ( x + a ) + C x + a ln ( ( x + a ) 2 + 1 ) + ( 2 a 2 − 1 ) arctan ( x + a ) + C x+a\ln\!\big((x+a)^{2}+1\big)+(2a^{2}-1)\arctan(x+a)+C x + a ln ( ( x + a ) 2 + 1 ) + ( 2 a 2 − 1 ) arctan ( x + a ) + C x − a ln ( ( x + a ) 2 + 1 ) + ( 2 a 2 + 1 ) arctan ( x + a ) + C x-a\ln\!\big((x+a)^{2}+1\big)+(2a^{2}+1)\arctan(x+a)+C x − a ln ( ( x + a ) 2 + 1 ) + ( 2 a 2 + 1 ) arctan ( x + a ) + C x − a 2 ln ( ( x + a ) 2 + 1 ) + ( 2 a 2 − 1 ) arctan ( x + a ) + C x-\tfrac{a}{2}\ln\!\big((x+a)^{2}+1\big)+(2a^{2}-1)\arctan(x+a)+C x − 2 a ln ( ( x + a ) 2 + 1 ) + ( 2 a 2 − 1 ) arctan ( x + a ) + C Browse the problem library