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【答案】应助回帖
★ ★ ★ ★ ★
感谢参与，应助指数 +1
airbaylor(feixiaolin代发): 金币+5 2014-08-24 22:10:55
feixiaolin: 数学EPI+1, elastic 2014-09-10 16:48:01
MATLAB的计算结果：
> syms x
int('(x^3+1)^(-1/2)',x)
ans =
((3^(1/2)*i + 3)*((x + (3^(1/2)*i)/2 - 1/2)/((3^(1/2)*i)/2 - 3/2))^(1/2)*((x + 1)/((3^(1/2)*i)/2 + 3/2))^(1/2)*((1/2 + (3^(1/2)*i)/2 - x)/((3^(1/2)*i)/2 + 3/2))^(1/2)*ellipticF(asin(((x + 1)/((3^(1/2)*i)/2 + 3/2))^(1/2)), -((3^(1/2)*i)/2 + 3/2)/((3^(1/2)*i)/2 - 3/2)))/(- (3^(1/2)*(i/2) - 1/2)*(3^(1/2)*(i/2) + 1/2) - x*((3^(1/2)*(i/2) - 1/2)*(3^(1/2)*(i/2) + 1/2) + 1) + x^3)^(1/2)
>> a=int('(x^3+1)^(-1/2)',x)
a =
((3^(1/2)*i + 3)*((x + (3^(1/2)*i)/2 - 1/2)/((3^(1/2)*i)/2 - 3/2))^(1/2)*((x + 1)/((3^(1/2)*i)/2 + 3/2))^(1/2)*((1/2 + (3^(1/2)*i)/2 - x)/((3^(1/2)*i)/2 + 3/2))^(1/2)*ellipticF(asin(((x + 1)/((3^(1/2)*i)/2 + 3/2))^(1/2)), -((3^(1/2)*i)/2 + 3/2)/((3^(1/2)*i)/2 - 3/2)))/(- (3^(1/2)*(i/2) - 1/2)*(3^(1/2)*(i/2) + 1/2) - x*((3^(1/2)*(i/2) - 1/2)*(3^(1/2)*(i/2) + 1/2) + 1) + x^3)^(1/2)
>> pretty(a)
1/2 / x - 1/2 + #3 \1/2 / 1/2 - x + #3 \1/2 / 3/2 + #3 \
(3 + 3 i) | ------------ | #2 | ------------ | ellipticF| asin(#2), - -------- |
\ #3 - 3/2 / \ 3/2 + #3 / \ #3 - 3/2 /
-----------------------------------------------------------------------------------------
3 1/2
(x + (- #1 - 1) x - #1)
where
#1 == (#3 - 1/2) (#3 + 1/2)
/ x + 1 \1/2
#2 == | -------- |
\ 3/2 + #3 /
1/2
3 i
#3 == ------
2 |
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