First Year College Calculus Question?

Question

Please Help me on this one.

∫ t cos(t) dt

Answer 1

∫ t cos(t) dt

Let    t = U and cos(t) =V  then it is in the form of   ∫ UV dV

∫ UV dV = U ∫ VdV - ∫ [ ∫ VdV d/dV(U)] dV

t ∫ cos(t) dt - ∫ [ ∫ cos(t) dt (d/dt)t] dt

t sin(t) - ∫[ sin(t) (1)] dt

t sin(t) - ∫ sin(t)dt

t sin(t) - (-cos(t)) + constant

t sin(t) + cos(t)) + constant

∫ t cos(t) dt = t sin(t) + cos(t)) + constant

 

I hope this will help you!!!