一道定积分的题目帮下忙啊
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没有上限和下限，这是不定积分！！
令x=z^6，dx=6z^5dz
∫√x/(1+x^1/3) dx
= 6∫z^8/(z²+1) dz
z^8 = z^6(z²+1-1) = z^6(z²+1) - z^6
z^6 = z⁴(z²+1-1) = z⁴(z²+1) - z⁴
z⁴ = z²(z²+1-1) = z²(z²+1) - z²
z²/(z²+1) = (z²+1-1)/(z²+1) = 1-1/(z²+1)
z^8/(z²+1) = z^6 - z⁴ + z² - 1 + 1/(z²+1)
原式= 6[z^7/7 - z^5/5 + z³/3 - z + arctanz] + C
= (6/7)x^(7/6) - (6/5)x^(5/6) + 2√x - 6x^(1/6) + 6arctan[x^(1/6)] + C
令x=z^6，dx=6z^5dz
∫√x/(1+x^1/3) dx
= 6∫z^8/(z²+1) dz
z^8 = z^6(z²+1-1) = z^6(z²+1) - z^6
z^6 = z⁴(z²+1-1) = z⁴(z²+1) - z⁴
z⁴ = z²(z²+1-1) = z²(z²+1) - z²
z²/(z²+1) = (z²+1-1)/(z²+1) = 1-1/(z²+1)
z^8/(z²+1) = z^6 - z⁴ + z² - 1 + 1/(z²+1)
原式= 6[z^7/7 - z^5/5 + z³/3 - z + arctanz] + C
= (6/7)x^(7/6) - (6/5)x^(5/6) + 2√x - 6x^(1/6) + 6arctan[x^(1/6)] + C
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