Since f(x)=\int xe^{-x^{2}}\d x, let u=-x^2, \d u=-2x\d x or \dfrac {-\d u}{2}=x\d x. Thus, f(x)=\int e^{u}\left(-\dfrac {\d u}{2}\right)=-\dfrac {1}{2}e^{u}+C=-\dfrac {1}{2}e^{-x^{2}}+C and f(0)=1 ⇒ - 12(e^0)+C=...
( e^(x+e^x)) 相关知识点: 试题来源: 解析 Write ( e^(x+e^x)) as a function. ( f(x)=e^(x+e^x)) 该填空题需要一个表示让步关系的连词,连接两个句子,表达“尽管父母总是要求我不要做某些事,但我仍然知道他们爱我”。合适的连词是“Although”,表示虽然,尽管,符合句子的语境和意思。反馈...
An antiderivative of f(x)=F(x) =int[log(logx)+(logx)^(-2)]dx+c =xlog(logx)-int(x)/(xlogx)dx+int(logx)^(-2)dx+c Integrating by parts in the first integral =xlog(logx)-[x(logx)^(-1)+int(logx)^(-2)dx]+int(logx)^(-2)dx+c [Again integrating by parts
Find the antiderivative of f(t) = \frac{3}{t} - \frac{2}{t^2}. Find the antiderivative of g(x) = -8e^{x + 4} - \frac{5}{x + 7} - 5 \sec^2 (x+6). Find the antiderivative of F(x) = \dfrac{x^2 +3x^3 -x^4}{x^5}. Find the antiderivative of e^{-0.5t} ...
{eq}\displaystyle \int\frac {e^x + e^{3 x}} {e^x}\ dx {/eq}. Integration The process of finding a function given its derivative is known as antiderivative. It is also known as integration. If {eq}\displaystyle F'(x)=f(x), {/eq} we say that {eq}...
In summary, the conversation discusses the evaluation of the anti derivative of e^x^2 as a Taylor Series. The conversation also mentions the use of the formula \frac{f^(n)(a)}{n!}(x-a)^n and the importance of using parentheses when writing e^x^2 to avoid confusion. The individual...
antiderivative the antiderivative of a function f is any function f which is differentiab1e and satisfies f t f t at a11 points in the domain of f p 115Exponential growth Some biological systems can be modeled using the idea of exponential growth. This means the variable of interest, x, ...
Find the most general antiderivative of the function:(Check your answer by differentiation.) g (v) = 5 + 3 sec^2 v. What is the antiderivative of the function f(x) = tan^2 (x) + (2x - 3)^5? Find the general antiderivative of the given problem...
Find the antiderivative of the function and show how to differentiate the function. log_a x. Find the antiderivative of the function and show how to differentiate the function. e^x. Find the antiderivative of the function and show how to differentiate the function. a^x...
We are exploring the antiderivative of the mathematical expression e√x / √x. By employing a variable substitution (u = √x), we can simplify the expression and find the derivative du/dx. Through a series of algebraic manipulations, we isolate dx and re