What is the antiderivative of the function f(x) given by f(x)=x*e^8x ?

Expert Answers

An illustration of the letter 'A' in a speech bubbles

The antiderivative of f(x)=x*e^8x can be found using integration by parts.

Int [u dv ]= u*v - Int[ v du]

Let u = x => du = 1

dv = e^8x => v = e^8x/8

Int [ x*e^8x ]  = (x*e^8x)/8 - Int [1*(e^8x)/8]

=> (x*e^8x)/8 - (e^8x)/64

The anti-derivative is (x*e^8x)/8 - (e^8x)/64 + C

Approved by eNotes Editorial Team
Soaring plane image

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial