U-Substitution, Integration by Parts and Differential Equations (8 Problems)
Please show all of the steps needed to solve the 8 integrals and differential equations that are attached.
The integral of x(cos(x) dx
The integral of (x^3) sin(x) dx
The integral of t(csc(t))cot(t) dt
The integral of arctan x dx
The integral of e^2x sin(X) dx
Solve the differential equation.
y’ = xe^x2
dy/dt = y^2/sqrt(2 + 3t)
cos(y) * y’ = 2x.