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what is the integral of lnx?
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lonewolf i think i am wrong but i need your verification on that.Originally posted by loop quantum gravity
i got it, thanks.
edit: just one problem shouldn't this be ∫u*dv/dx=∫1 ?
The integral of lnx, also known as the natural logarithmic function, is the inverse of the derivative of lnx. It represents the area under the curve of the function y=lnx from a given interval.
The integral of lnx can be calculated using the integration technique known as integration by parts, where u=lnx and dv=dx. The formula for integration by parts is ∫udv = uv - ∫vdu. By plugging in u=lnx and dv=dx, the integral can be solved step by step.
The integral of lnx is important in mathematics as it has many applications in various fields such as physics, economics, and engineering. It is used to solve problems involving rates of change, growth and decay, and optimization.
Yes, the integral of lnx can also be solved using substitution or other integration techniques such as u-substitution. However, integration by parts is the most commonly used method for solving this integral.
Yes, the interval for solving the integral of lnx is typically from 0 to infinity. This is because the natural logarithmic function is undefined for negative numbers and the integral is only valid for positive intervals.