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    U-Substitution, Integration by Parts and Differential Equations (8 Problems)

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    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.

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    Solution Summary

    This solution shows how to calculate the integrals for the eight problems.