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58问答库 > x∧4+x∧3√（1+x∧2）的定积分是什么？

x∧4+x∧3√（1+x∧2）的定积分是什么？

2025-03-16 21:12:10

推荐回答（1个）

回答（1）：

∫[ x^4+x^3.√（1+x^2）] dx
= (1/5)x^5 +∫x^3.√（1+x^2） dx
=(1/5)x^5 +(1/3)∫x^2.d(1+x^2)^(3/2)
=(1/5)x^5 +(1/3)x^2.(1+x^2)^(3/2) -(2/3)∫x(1+x^2)^(3/2) dx
=(1/5)x^5 +(1/3)x^2.(1+x^2)^(3/2) -(2/15)(1+x^2)^(5/2) + C

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