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

 

[vds700]

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

=(1/2)(3x^2 - 4x + 3)e^(x^3-2x^2+3x-5)
let u = x^3-2x^2+3x-5
du/dx = 3x^2 -4x + 3
du = (3x^2 - 4x + 3)dx

therefore the integral is

I (1/2)e^udu
=(1/2) e^u + c
=(1/2)e^(x^3-2x^2+3x-5) + c

 

[jaychouf4n]

Thank you

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]

 

[tommykins]

回复: Re: Exponential Question

Or by inspection

the top is in the form of f'x

so the integral is f'x/fx

= ln fx where fx = e^x + e^-x

 

[Aerath]

Re: 回复: Re: Exponential Question

Just wondering - would you lose marks for forgetting +C?

 

[jaychouf4n]

thanks

ARGH

another question xD

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

a^x+ax

 

[tommykins]

回复: Re: Exponential Question

Just wondering - would you lose marks for forgetting +C?

If it's a 1-2 marker, yes. If not, probably unlikely. Get accustomed to it though.

thanks

ARGH

another question xD

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

a^x+ax

int a^x + ax = a^x.lna + ax^2/2 + c

 

[jaychouf4n]

Hey how can i show that

xe^x=e^(x+log x)

 

[lyounamu]

Hey how can i show that

xe^x=e^(x+log x)

R.H.S. = e^(x+log x) = e^(log(e^x)+logx)
= e^(log(e^x . x)
= e^x . x = L.H.S.

OR

L.H.S. = e^x . x = e^(log(x)) . e^(log(e^x)
= e^(log(x) + log(e^x))
= e^(log(x) + x)
= R.H.S