∫ (x^7/（x^4+2))dx,求不定积分_数学解答

∫ (x^7/（x^4+2))dx,求不定积分

人气：242 ℃　时间：2020-04-09 07:35:47

解答

答：∫[x^7/(x^4+2)]dx
=∫[(x^4)*(x^3)/(x^4+2)]dx
=(1/4)∫[(x^4+2-2)/(x^4+2)]d(x^4+2)
=(1/4)∫[1-2/(x^4+2)]d(x^4+2)
=(x^4+2)/4-(1/2)ln(x^4+2)+C1
=(x^4)/4-(1/2)ln(x^4+2)+C