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U-Substitution and Integration by Parts and Differential Equations (6 Problems)

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Please show all of the steps needed to solve the 6 integrals and differential equations that are attached.

A. 3/sqrt(6x - x^2) dx
B. 4/(4x^2 + 4x + 65) dx

Solve the differential equation.

1. dy/dx = (1 + e^x)^2
2. dr/dt = (1 + e^t)^J/e^t
4. (4 + tn^2x)y' = sec^2 x
5. y' = 1/(x*sqrt(4x^2 - 1))

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This solution shows how to integrate using substitution or integration by parts in an attached Word document.

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