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=...
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...
Find the antiderivative of the function. f(x) = 7e^x a) e^{7x} b) \frac {1}{7}e^{7x} What is the integral to: \int \frac {2x^2 - 3x + 1}{x(x^2 - 1)(x - 2)^3(x^2 + 4)^2} dx Find the antiderivative of f(x) = fraction {1}{(2x+1)^3} ...
Find the antiderivative: dy/dx = x - e^x. Find the antiderivative. \int xe^{1-x^2} dx Find the antiderivative of 7x^3. Find the antiderivative: int dfrac{1}{10+x^2+2x} dx. Find the antiderivative F (x) of f (x) = x / {3 (12 x^2 - 6)}, given F (1) = 5. Find...
Find the antiderivative: int x2 + 9 x3 - 9x dx Find the antiderivative. \int \sqrt[4]{10w}dw Find the antiderivative. int 7cos(2x)-5sin(3x)dx Find the antiderivative. int frac{1}{sqrt{9xdx Find the antiderivative of \frac{1}{x^2 - x + 1} , i.e., \int \frac{1}{x^...
Find the particular antiderivative of the following derivative that satisfies the given condition. dx} \over {dt = 2{e^t} - 3, \quad x\left( 0 \right) = 1 Find the particular antiderivative of the following derivative that satisfies the given condition. ...
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
Example 1: a) Write {eq}3^x = 7 {/eq} as a log. b) Write {eq}\log_9x = 3 {/eq} as a power expression. Lesson Quiz Course 12Kviews What is a Natural Logarithm Definition? A natural logarithm is a logarithm of base {eq}e {/eq}, and it is customary to write a natural ...
Find an antiderivative F(x) of f(x) = 11x - \sqrt x. Find the antiderivative for f(x) = \frac{2x^2 + x + 9}{(x - 1)(x^2 + 3)} Find the antiderivative f(x) = 2 x^{-4} for x > 0 Find an antiderivative F(x) with F'(x) = f(x) and F(0) = 0 ...
What is the antiderivative of the function f(x) = tan^2 (x) + (2x - 3)^5? Find the general antiderivative of the given problem. f(x) equals e^{5x} - secx tan(x/2) Find the most general antiderivative of sec^2 x + cos x. (a) = 1 / ...