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=...
Find the antiderivative F (x) of f (x) = x / {3 (12 x^2 - 6)}, given F (1) = 5. Find an antiderivative of f(x). 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...
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} ...
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...
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
\ x(t) = \boxed{\space}. 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...
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 / 3...
A natural logarithm is a logarithm of base {eq}e {/eq}, and it is customary to write a natural log as {eq}\ln(x) = y {/eq} instead of {eq}\log_ex = y {/eq}. In math, {eq}e {/eq} is Euler's constant or theexponential. It is an irrational number that equals approxi...
Find the antiderivative of e^{-0.5t} + 1 Find the antiderivative. \int xe^{1-x^2} dx Find the antiderivative of g(x) = -8e^{x + 4} - \frac{5}{x + 7} - 5 \sec^2 (x+6). Find the antiderivative. f(x) = \frac{6}{5}csc^2 (\frac{x}{5}) Find the ...
Expand the integral and then find an antiderivative: \int (x^2+3x-2)^2 dx Find the indefinite integral. (Use C for the constant of integration.) integral {e^{3 x} + 3 e^x + 3} / {e^x} dx Find the integral: integral (1 - 6 x) e^{3 x -...