∫ (x^7/(x^4+2))dx,求不定积分
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/07/27 22:08:59
∫ (x^7/(x^4+2))dx,求不定积分
![∫ (x^7/(x^4+2))dx,求不定积分](/uploads/image/z/15998331-3-1.jpg?t=%E2%88%AB+%28x%5E7%2F%EF%BC%88x%5E4%2B2%29%29dx%2C%E6%B1%82%E4%B8%8D%E5%AE%9A%E7%A7%AF%E5%88%86)
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
=∫[(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