Find the general solution xt for the following differential

Question

Problem 1) : Find the indefinite integralv(t)=∫(t^2 )dt

Problem 2) : Find the indefinite integralv(x)=∫(t^2 )dx

Problem 3) : Find the indefinite integralv(x)=∫(3x^2+2/x^2 -3/x+2)dx

Problem 4) : Find the general solution x(t) for the following differential equation x'(t)=t^3/3.

Problem 5) : Find the particular solution x(t) for the following differential equation x'(t)=t^3/3 with initial condition x(t=1)=2.

Problem 6) :Find x(t) solution for indefinite integral x(t)=∫(t+1)dt with x(t=0)=2.

Problem 7) :Evaluate definite integral x=_(t=0)∫^(t=2)(t^3-1) dt. It is similar to x=₀∫²(4t^3-1) dt

Problem 8) :Evaluate definite integral x(t)=∫_(t=0)^t(4t^3-1) dt. The upper limit is variable t.

Problem 9) :Find the derivative v(t)=d/dt x(t) where x(t)=t^2+t^(-2)-3t-2.

Problem10) :Find the derivative a(t)=d/dt v(t) where v(t) is from problem 9.