∫ x e^x dx (by parts: u = x, dv = e^x dx):
Ae^x × x²
Bx e^x - e^x + C = e^x (x - 1) + C
Ce^x / x
Dx² e^x
Answer & Solution
Correct answer: B. x e^x - e^x + C = e^x (x - 1) + C
u = x, du = dx; dv = e^x dx, v = e^x. ∫ x e^x dx = x e^x - ∫ e^x dx = x e^x - e^x + C = (x - 1) e^x + C.
Related questions
The definite integral of f from a to b is a:In integration by substitution, the aim is to rewrite the integrand in a form that is:For a negative value of C, the parabola's vertex lies on the y-axis on the side that is:Shifting the parabola y equals x squared one unit up gives the member with C equal to:The geometrical interpretation of an indefinite integral is a family of:Indefinite integrals were studied before the section on integrals that are:The two ways of introducing the definite integral are limit of a sum and:The Fundamental Theorem of Calculus is introduced through a function called the: