2023年4月8日 · Answer: The integration of e^x^2, e to the x square, is equal to root (pi)/2 × erfi (x)+C where erfi (x) is the “imaginary error function”. Note that ∫ e x 2 d x = x + x 3 3 + x 5 10 + ⋯ + C.

∫ − ∞ ∞ e − x 2 d x \displaystyle\int_{-\infin}^{\infin}e^{-x^2}dx ∫ − ∞ ∞ e − x 2 d x 是一个比较常见的无穷积分，在许多领域有着重要应用。 在此介绍几种巧妙的解法，供读者欣赏。

For example, you can express $\int x^2 \mathrm{d}x$ in elementary functions such as $\frac{x^3}{3} +C$. However, the indefinite integral from $(-\infty,\infty)$ does exist and it is $\sqrt{\pi}$ so explicitly: $$\int^{\infty}_{-\infty} e^{-x^2} = \sqrt{\pi}$$

2016年4月30日 · To integrate x to a power times e to a power, we expect to differentiate the x and integrate the e to a power. ∫x2ex2dx. In order to integrate ex2dx we need an x so that we can use substitution. ∫x2ex2dx = ∫xex2 xdx . Let u = x and dv = ex2 xdx. The du = 1dx and v = 1 2ex2. ∫x2ex2dx = 1 2 xex2 − 1 2∫ex2dx. Now we need to stop.

2015年4月27日 · How do you find the integral of ex2? Use some kind of approximation method. There is no nice, finitely expressible antiderivative. (Other that to write: ∫ex2dx, of course.) One …

\int e^xsinxdx=\frac{e^x(sinx-cosx)}{2}+C. 该方法可谓妙哉，其中的技巧性值得读者玩味。而且可以扩展到 \int e^{\alpha x}sin(\beta x+\varphi)dx （其中，α，β， \varphi 均为给定的常量） （PS：cos相当于sin(x+ \frac{\pi}{2})，当然，亦可不做变换直接计算，过程类似）

ex2 : 外部中断2(int2)中断允许位，ex2=1允许中断，ex2=0禁止中断。外部中断2(int2)同 样只能部降沿下降触发。itn是控制是上沿还是下沿触发，比如外部中断1. it1：外部中断1中断源类型选择位。it1=0，int1/p3.3引脚上的上升沿或下降沿信号均可触发 外部中断1。

2015年12月2日 · There is no simple closed form for the Error function in terms of elementary functions such as polynomial, exponential or trigonometric functions. Through a little manipulation, you can show that 2 π√ ∫x 0 et2 dt = i erf(ix) 2 π ∫ 0 x e t 2 d t = i erf (i x), which is known as the imaginary Error function.

We will use the formula of ∫ x n = x n + 1 n + 1 and we will integrate each of them. = C + x + x 3 3 + x 5 10 + x 7 42 +... We can see that we don’t get any feasible finite solution for the given problem. In the above solution we solved the integration for e x 2 but we get an infinite solution.

∫ e a x d x = 1 a e a x . {\displaystyle \int \text{e}^{ax} \mathrm{d}x … 这里列举了一些有关指数函数的不定积分公式，以下例子中均省略积分常数，且限定积分和结果均在被积函数定义域的内点的邻域中。