Monday, May 20, 2013

Single Variable Calculus, Chapter 8, 8.1, Section 8.1, Problem 52

Use the formula xnexdx=xnexnxn1exdx to find x4exdx


x4exdx=x4ex4x3exdx=x4ex4(x3ex3x2exdx)=x4ex4x3ex+12(x2ex2xexdx)=x4ex4x3ex+12x2ex24(xexx0exdx)=x4ex4x3ex+12x2ex24xex+24ex+c=ex(x44x3+12x224x+24)+c

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