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))
Please see the attached file for the full solution.
This solution shows how to integrate using substitution or integration by parts in an attached Word document.