高数问题，第19题，谢谢啦，希望在纸上写了拍上来
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∫(x²+1)/(x⁴+1)dx
=∫(x²+1)/(x⁴+2x²+1-2x²)dx
=∫(x²+1)/[(x²+1)²-2x²]dx
=∫(x²+1)/[(x²+1-√2x)(x²+1+√2x)]dx
=1/2∫1/(x²+1-√2x)+1/(x²+1+√2x)]dx
=∫1/[(√2x-1)²+1]+1/[(√2x+1)²+1]dx
=1/√2arctan(√2x-1)+1/√2arctan(√2x+1)+C
=∫(x²+1)/(x⁴+2x²+1-2x²)dx
=∫(x²+1)/[(x²+1)²-2x²]dx
=∫(x²+1)/[(x²+1-√2x)(x²+1+√2x)]dx
=1/2∫1/(x²+1-√2x)+1/(x²+1+√2x)]dx
=∫1/[(√2x-1)²+1]+1/[(√2x+1)²+1]dx
=1/√2arctan(√2x-1)+1/√2arctan(√2x+1)+C
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