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I'm working on an infinite series problem and need to find the antiderivative of 1/((x(lnx)^3). Homework Equations u=lnx The Attempt at a Solution I know I have to use the substitution u=lnx, but I still can't figure out what the answer is. I know the antiderivative of 1/((x(lnx)) is ln(lnx) but the third power in my problem is giving me trouble.
The antiderivative of 1/sqrt(lnx - c) is 2/sqrt(lnx - c) + C, where C is the constant of integration. 2. Can the antiderivative of 1/sqrt(lnx - c) be simplified? Yes, the antiderivative can be simplified to 2√(lnx - c) + C. 3. Is it possible to find the antiderivative of 1/sqrt(lnx - c) analytically? Yes, it is possible to find the ...
Apr 30, 2008. In summary, the conversation was about finding the antiderivative of 2 (1 + lnx) (x^x)^2, which initially seemed unsolvable. However, the solution was found using substitution and the answer is (x^x)^2. One of the participants also mentioned the importance of using LaTeX in math discussions. Apr 30, 2008. #1.
Yes, we can use the definite integrals property to solve the integral of e^x. (lnx)dx. By using the property ∫a^b f (x) dx = F (b)-F (a), where F (x) is the antiderivative of f (x), we can evaluate the definite integral by plugging in the limits of integration into the antiderivative formula.
How can I evaluate the integral of x/lnx if all methods seem to fail? In summary: It is possible that the exponential integral function itself is not "elementary".In summary, The problem discussed is evaluating the integral \int \frac {x} {ln (x)} dx, which has a solution of \frac {1} {2} \frac {x^2} {ln (x)} according to Maple. However, this ...
The solution of the integral 1/lnx is ln(lnx) + C, where C is the constant of integration. This can be verified by differentiating the solution and using the chain rule, which gives 1/lnx * 1/x = 1/(x*lnx). 2. How do you solve the integral 1/lnx? To solve the integral 1/lnx, you can use the substitution method. Let u = lnx, then du = 1/x dx.
Yes, the integral 1/x log (x) or lnx can be solved analytically using integration by parts. This method involves breaking down the integral into simpler parts and using a formula to solve each part. However, the resulting integral may still be difficult to evaluate without the use of numerical methods. 3. How is the integral 1/x log (x) or lnx ...
In summary, the antiderivative of 1/x can be expressed as ln(x) or ln(|x|), depending on the domain of the function. Both ln(x) and ln(|x|) are valid antiderivatives and differ by a constant. However, if the function has a discontinuity at x=0, ln(x) should be used as the antiderivative.
The definite integral of 1/ln (x) does not exist because the function 1/ln (x) is not defined for x ≤ 1. Since the domain of the function is limited, it cannot be integrated over an infinite interval, and therefore the definite integral does not exist.
chemical. 14. 0. ive been trying to do this problem and its annoying! The function to be integrated: 1 + 1/x + x dx. Interval: [8,2] when anti differentiating the fuction i get x + x^2/2 + lnx but i don't think the integral of 1/x is lnx...help would be appreciated. Last edited: May 9, 2004.