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Phys_Boi
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Homework Statement
∫(1+(1/x))^x dx
Homework Equations
How do I integrate this compound interest e approximation
The Attempt at a Solution
Inside: x + ln(|x|) + C
Outside: (a^x)/(ln(a))
Thanks. I'm new and don't know a lot.. However the ti-84 will give me a value for a definite integral. I don't know how.mfb said:I would be extremely susprised if it has a closed form for the integral.
Phys_Boi said:Thanks. I'm new and don't know a lot.. However the ti-84 will give me a value for a definite integral. I don't know how.
The expression "Integrate (1+(1/x))^x" refers to finding the antiderivative or the indefinite integral of the function (1+(1/x))^x. In other words, it involves the process of finding a function whose derivative is equal to (1+(1/x))^x.
Yes, (1+(1/x))^x is a continuous function. It is a composition of continuous functions (1+x) and x^x, which makes it continuous for all real values of x.
The domain of (1+(1/x))^x is all real numbers except x = 0. The range of this function is (1, +∞), which means it takes on all positive values greater than 1.
No, (1+(1/x))^x cannot be integrated using basic integration techniques such as power rule, substitution, or integration by parts. It requires advanced techniques such as integration by parts with logarithmic functions to find the antiderivative.
The integral of (1+(1/x))^x has various applications in physics, engineering, and finance. For example, it can be used to calculate the area under a curve, the volume of a solid of revolution, or the accumulated interest for continuously compounded investments. Additionally, it is also used in probability and statistics to calculate the cumulative distribution function of certain distributions.