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gulsen
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[tex]\int \frac{dx}{\sqrt{1/x + C}}[/tex] where C is a constant. Any ideas?
HallsofIvy said:Is that [tex]\frac{1}{x}+ C[/tex] or [tex]\frac{1}{x+C}[/tex]?
No, we did not say that:gulsen said:Easily??
Well, the previous ones seem to be wrong, I got this monster from mathematica:
[tex]\frac{cx+1}{c \sqrt{c + \frac{1}{x}}} - \frac{\sqrt{cx+1} asinh {\sqrt{cx}} }{c^{3/2} \sqrt{c + \frac{1}{x}} \sqrt {x}}[/tex]
BTW, how did you guys derieved [tex]\int\sqrt{x+C}dx[/tex] from [tex]\int\sqrt{\frac{x}{1+Cx}} dx[/tex]?
Very good question, misskitty!misskitty said:How can you write 1 + Cx when the original is 1/x + C? Pardon my ingnorance on this subject, but we just started these last week.
The integral of a function is a mathematical concept that measures the area under the curve of a function. It is represented by the symbol ∫ and is used to find the total amount of a quantity over a certain interval.
The integral of a function is calculated using integration, which is the reverse process of differentiation. It involves finding the anti-derivative of the function and evaluating it at the upper and lower limits of the interval.
A definite integral has specific limits of integration and gives a single numerical value as the result. An indefinite integral, on the other hand, does not have limits and gives a function as the result, which can be further evaluated for specific values.
The integral of a function has many applications in mathematics, physics, and engineering. It is used to calculate areas, volumes, and other quantities that can be represented by a function. It also helps in solving differential equations and finding the average value of a function over an interval.
There are several techniques for evaluating integrals, such as substitution, integration by parts, partial fractions, and trigonometric substitutions. Choosing the right technique depends on the form of the function and the limits of integration.