integrate [xe^(-x)] with respect to x.
integrating a product of functions of x - integration by parts. integral of uv' = uv - integral of u'v. choice of u from LIATE - logs, inverse trig, algebra, trig, exponentials - choose u=x. u=x, v'=e^(-x). to find u', differentiate u. u' = 1. to find v, integrate v'. v = -e^(-x). we now have everything we need to integrate by parts; integral of uv' = uv - integral of u'v => integral of xe^(-x) = -xe^(-x) - integral of -e^(-x) = -xe^(-x) - e^(-x) + c = -(x+1)e^(-x) + c
ZP
Related Maths A Level answers
All answers ▸Solve the following definite integral: f(x)=3e^(2x+1) for the limits a=0 and b=1, leaving your answer in exact form.
Express √75 in the form of n√3 , where n is an integer. Using this information, solve the following equation: x√48 = √75 + 3√3 (4 marks)
integrate with respect to x the function f(x)= xln(x)
Use integration by parts to find ∫ (x^2)sin(x) dx. (A good example of having to use the by parts formula twice.)