kill00 said:Homework Statement
what is the integral of ln(e2x-1) dx
2. The attempt at a solution
I got
u= ln(e2x-1)
du = 2e2x-1 \ e2x-1
du = 2 dx
1/2(integral of u du)
1/2 ln (e2x-1 ) +c
=
1/4 [ln (e2x-1 )]2 + c
Could you please let me know if this is correct? I don't know how to integrate ln
thanks again
The natural log, or ln, is a logarithmic function that is the inverse of the exponential function. It is written as ln(x) and represents the power to which the base e (approximately equal to 2.718) must be raised to equal x.
Integrating natural log problems allows us to find the area under a curve and solve for the original function. This is useful in many fields of science, such as physics and biology, where finding the total change or growth over time is important.
The basic rules for integrating natural log include: using the power rule, integrating by parts, and using the substitution method. It is also important to remember that ln(x) integrates to 1/x and ln(ax) integrates to (1/a)ln(ax) + C.
To solve a natural log integration problem, you can follow these steps: 1. Identify the function to be integrated. 2. Use the appropriate integration rule based on the form of the function. 3. Simplify the expression, if possible. 4. Add a constant of integration, denoted by +C.
Yes, natural log integration problems can have multiple solutions. This is because the constant of integration (+C) can take on any real value, resulting in an infinite number of possible solutions. To find the specific solution, additional information or boundary conditions are needed.