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poopforfood
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Homework Statement
Integral of sqrt(x-1)/sqrt(x)
Homework Equations
The Attempt at a Solution
I think I have to sub x = sinh2 so you get sqrt(1-sinh2)/sqrt(sinh2)
I forget what to do after this
The integral of sqrt(x-1)/sqrt(x) is equal to 2*sqrt(x-1) + C, where C is a constant of integration. This can be found by using the u-substitution method and letting u = sqrt(x-1).
The process for solving this integral involves the use of u-substitution. First, let u = sqrt(x-1). Then, rewrite the integral as 2*u/sqrt(x). Next, use the power rule to integrate, giving us 2*u^(3/2)/3 + C. Finally, substitute back in the original variable, giving us the final answer of 2*sqrt(x-1) + C.
Yes, for this integral you will need to know the u-substitution method and the power rule for integration. It is also helpful to have knowledge of basic integration techniques such as integration by parts and trigonometric substitution.
Yes, this integral can also be solved using integration by parts or trigonometric substitution. However, the u-substitution method is the most straightforward and efficient way to solve this particular integral.
Sure, let's say we want to find the integral of sqrt(x-1)/sqrt(x). First, let u = sqrt(x-1). Then, the integral becomes 2*u/sqrt(x). Next, we use the power rule to integrate, giving us 2*u^(3/2)/3 + C. Finally, we substitute back in the original variable, giving us the final answer of 2*sqrt(x-1) + C.