- #1
donleo
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Homework Statement
Integrate e^2x / SQRT [(e^2x) + 3)]
Homework Equations
The Attempt at a Solution
i know the solution, is: SQRT [(e^2x) + 3]
but i have no idea why. Please I need help
thank you
eok20 said:Have you tried substitution?
eok20 said:Ok, if t=e^2x + 3 then dt = 2e^2x, and what does the integral become in terms of t and dt?
eok20 said:Close, you have 1/2(dt/sqrt(t)) = 1/2 t^(-1/2) dt. You integrated 1/2 t^(1/2) dt instead
The function "Integrate e^2x / SQRT (e^2x + 3)" is an integral function that calculates the area under the curve of the expression e^2x / SQRT (e^2x + 3).
The domain of the function "Integrate e^2x / SQRT (e^2x + 3)" is all real numbers, and the range is also all real numbers.
The derivative of the function "Integrate e^2x / SQRT (e^2x + 3)" is e^2x / (e^2x + 3)^(3/2).
The integral of the function "Integrate e^2x / SQRT (e^2x + 3)" is (1/2)(e^2x + 3)^(1/2) + C, where C is the constant of integration.
The function "Integrate e^2x / SQRT (e^2x + 3)" can be used in various fields of science, such as physics and engineering, to calculate areas under curves and to solve differential equations. It can also be used in finance and economics to calculate the change in value over time.