企源知识库

求∫[x(1+x)²/(1+x⁴)]dx
【正确答案】：∫[x(1+x²)/(1+x⁴)]dx=∫[x/(1+x⁴)]dx+∫[x³/(1+x⁴)]dx=1/2∫[x=1/(1+(x²)²]d(x²)+1/4∫[1/(1+x⁴)]d/(1+x⁴)=(1/2)arctanx²+(1/4)ln(1+x⁴)+C