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
That is, the function F(x) is the antiderivative of f(x) if F'(x) = f(x). What is the antiderivative used for? An antiderivative can be used to "undo" a derivative, although some information is lost. It can also be used to find the area under a curve. What is the difference...
Verify that F(x) is an antiderivative of the integrand f(x) and use Part 2 of the Fundamental Theorem to evaluate the definite integral. Integral from 0 to 3 of (x^2 + 4x - 3) dx, F(x) = 1/3 x^3 + 2x^...
(∫ 1/(x√(x^2-1^2))dx) The integral of ( 1/(x√(x^2-1^2))) with respect to ( x) is ( (arcsec)(x)) ( (arcsec)(x)+C) The answer is the antiderivative of the function( f(x)=1/(x√(x^2-1))). ( F(x)=)( (arcsec)(x)+C)反馈...
Find the particular antiderivative of the following derivative that satisfies the given condition. dydx=3x−4+6x−1−1;y(1)=4 y(x) = Differential Equation: To find the antiderivative we will integrate the function that is we will separat...
For example, we need to find the antiderivative of x ln x. Then, according to the sequence above, the first function is ln x and the second function is x. Therefore, we have ∫x ln x dx = ln x ∫x dx - ∫[(ln x)' ∫x dx] dx ...
( f(x)=(ln)(x)dx) The function( F(x)) can be found by finding the indefinite integral of the derivative( f(x)). ( F(x)=∫ f(x)dx) Set up the integral to solve. ( F(x)=∫ (ln)(x)dxdx) Since ( d) is constant with respect to ( x), move ( d) out of the in...
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} ...
The antiderivative of∫ 1(√(1-x^2))dxcan be either arcsin x+C or - arccos x+C. Does th
Verify that F(x)=xln(x)−x is an antiderivative of ln(x). Proof of Anti-Derivative and By Parts Method: To prove the value of the anti-derivative of an integrand, we can apply the by parts method using the ILATE (inverse, logarithmic, algebraic, trigonometric, exp...