$sin(x^2)dx=？？？
（用$代表不定积分符号）

use sin(x^2)=1/2(1-cos2x)

sin(x)*sin(x)才等于1/2(1-cos2x)

I could tell you last semester but now i forget to how to deal with it. Haha, sorry about it!!!

<math width="200" height="300">
<param name="equation" value="\int\sin x^2 dx" />
</math>

(remember to choose "Use Huasing Code")

尝试用taylor series（不急得是不是这个名字了）打开，然后逐项积分。所以我猜没有精确代数解。

>> syms x
>> y=sin(x^2)

y =

sin(x^2)


>> int(y)

ans =

1/2*2^(1/2)*pi^(1/2)*FresnelS(2^(1/2)/pi^(1/2)*x)

>>


don't ask me what is "FresnelS()"

Integrate[Sin[x^2],x]= Sqrt[Pi/2]*FresnelS[Sqrt[Pi/2]*x]

Integrate[Sin[x^2],{x,-Infinity,Infinity}]= Sqrt[Pi/2]

这个函数好想属于积不出的.
这类函数还有$dx/lnx, $sin(x)dx/x, 虽然看起来很简单.不知道各位高手是怎么积出来的?都是一些看不懂的东东...

In indefinite integral, it is not integrable.
However in definite integral, by complex analysis,
\int_0^{\infty}\sin(x^2)dx=\sqrt{\pi}/(2\sqrt{2}).

BTW, the Fresnel integral is defined as
c(z)=\int_0^z\cos(\pi*t^2/2)dt.
So matlab and mathematica give solutions related with Fresnel integral.

sin (x^2)的taylor series是可以求出来的啊，所以，如果是不定积分的话，就可以通过泰勒级数找到一种数列的表达方法，如果是定积分的话，如果有精确度的限制，就能够求出答案来。