Another Exponential Question (1 Viewer)

[jaychouf4n]

How do i find the primitive for the function

(6x^2-8x+6)e^(x^3-2x^2+3x-5)

i.e. 13C 8 a)

and can you please explain the reasoning

 

[foram]

How do i find the primitive for the function

(6x^2-8x+6)e^(x^3-2x^2+3x-5)

i.e. 13C 8 a)

and can you please explain the reasoning

Let f(x) = x^3-2x^2+3x-5

Notice that (6x^2-8x+6) = 2 f'(x)

Therefore the question is in the form 2.f'(x).e^(f(x)

Therefore the primitive function is

2e^f(x)
=2e^(x^3-2x^2+3x-5)

 

[jaychouf4n]

Thanks!!

Another question

sorry XD

diffrentiate e^x+e^-x

That's e^x-e^-x

so how do i use this to find the definite integral of (e^x-e^-x)/(e^x+e^-x)

 

[Aerath]

Look at solution there.

 

[foram]

Thanks!!

Another question

sorry XD

diffrentiate e^x+e^-x

That's e^x-e^-x

so how do i use this to find the definite integral of (e^x-e^-x)/(e^x+e^-x)

f(x)=e^x+e^-x
f'(x)=e^x-e^-x

(e^x-e^-x)/(e^x+e^-x)= f'(x)/f(x)

Integral of f'(x)/f(x) = ln[f(x)]
ln(e^x+e^-x)+C

 

[jaychouf4n]

ARGH

another question xD

how do i use a=e^log a to find the primitive of

a^x+ax

 

[foram]

ARGH

another question xD

how do i use a=e^log a to find the primitive of

a^x+ax

a^x = e^xlna

Integral of a^x+ax = (e^xlna)/lna + (ax^2)/2 + C
=(a^x)/lna + (ax^2)/2 +C