 In this video, we provide the solution to question number 19 for the practice final exam for math 1210 We're asked to evaluate the indefinite integral of e to the sine of x times cosine of x dx This is a classic question of where we would want to use u substitution because notice if you take u to be sine of x Sine, of course, is the exponent of this exponents right here. That's a good choice for you du is going to be cosine of x dx Therefore our integral that is the integral of e sine of x times cosine of x dx by this u substitution It simplifies just to be e to the u du for which the anti derivative of e to the u would be e to the u plus a constant That is e to the u is its own anti derivative because e to the u is its own derivative Plugging back in that u is sine of x we get that the most general anti derivative would be e to the sine of x Plus a constant like so and it is important You remember the plus c because when you calculate indefinite integrals We're looking for the most general anti derivative and if you forget the plus c you'd have to lose a point So don't do that remember to have a plus c when you do indefinite integrals