Question

integral of (e^x)[(f(x))+(f'(x)]

Answer 1

e^xf(x)

Answer 2

can you explain the working ?

Answer 3

yea sure :)

Answer 4

http://www.twiddla.com/575173 u can use this ,its easier here :)

Answer 5

e^x f'(x) + e^xf(x)

first we will solve the first one

e^x f'(x)


Now do you know the by parts

Answer 6

I'm on twidlla

Answer 7

the terms f(x) and its prime,i dont know how to deal with them,and yes i know the 'by parts'

Answer 8

e^x (f(x)+f'(x)) if you factorize it is e^xf(x) +e^x(f'(x) now, you can see clearly that this is a derivative of e^x(f(x), because forming the derivative you have to use the product rule. Can you see it now?

Answer 9

Just look at the product rule, it is: (u,v)' = u'*v + u*v' , u and v being functions of x

Answer 10

Let look at \[{(e^x*f(x))'=(e^x)'f(x)+e^xf'(x) =e^xf()+e^xf'(x)=e^x(f(x)+f'(x))}\]
So we can say that
\[e^x(f(x)+f'(x))=(e^xf(x))'\]
\[\int\limits(f'(x)dx)=f(x)+C\]
Then \[\int\limits(e^x(f(x)+f'(x)))dx=\int\limits((e^xf(x))')dx=e^xf(x)+C\]

Answer 11

@Ishaan:thanks for all the help,and im sorry about leaving without informing,my power supply got heavily disrupted.
@ajahangir and tatiana: thankyou :)