Show that #intx²( e^x -1 )dx = x²e^x -2xe^x +2e^x -(x^3)/3 + c#?

1 Answer
Jan 9, 2016

Voilá

Explanation:

#I = intx^2(e^x-1)dx#

Rewriting it

#I = intx^2e^x - x^2dx#

#I = intx^2e^xdx - x^3/3#

For the first integral say #u = x^2# so #du = 2x# and #dv = v = e^x#

#I = x^2e^x - 2intxe^xdx - x^3/3#

Say that #u = x# so #du = 1# and #dv = v = e^x#

#I = x^2e^x - 2(xe^x - inte^xdx) - x^3/3#

#I = x^2e^x - 2xe^x + 2e^x - x^3/3 + c#