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## Homework Statement

I thought sometimes the integral of e^x is xe^x. Under what circumstances is the integral of e^x = xe^x? I think it has something to do with u substitution.

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- Thread starter robertjford80
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I thought sometimes the integral of e^x is xe^x. Under what circumstances is the integral of e^x = xe^x? I think it has something to do with u substitution.

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Ray Vickson

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## Homework Statement

I thought sometimes the integral of e^x is xe^x. Under what circumstances is the integral of e^x = xe^x? I think it has something to do with u substitution.

Under NO circumstances is the integral of e^x equal to x e^x. I cannot imagine why you think that would hold.

RGV

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what about the derivative?

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DryRun

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The derivative of [itex]e^x[/itex] is: [tex]e^x .\frac{d(x)}{dx}[/tex]

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HallsofIvy

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The

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DryRun

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Theonlyfunctions having the property that their derivative is equal to the function itself is a constant times [itex]e^x[/itex].

I don't think anyone could have explained it better. This should resolve your confusion, robertjford80.

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What's going on here? It clear says that the derivative of

c

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SammyS

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What's going on with the derivative of c

What's going on here? It clear says that the derivative of

c_{1}e^{(3/2)x[}= (3/2)c_{1}e^{(3/2)x}

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DryRun

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Correct, except for the integral of ##e^{2x}## which is ##\frac{e^{2x}}{2}##

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<deleted>

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{this referred to number nine's deleted post} i saw it before he deleted it.

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{this referred to number nine's deleted post} i saw it before he deleted it.

The chain rule is to multiply by the derivative, and the derivative of x is 1.

If it helps, d/dx (e

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thanks villyer, I hadn't thought about that.

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Ray Vickson

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No, the first statement is not right, and is not what you asked originally. The indefinite integral of exp(a*x) for constant a is (1/a)*exp(a*x) + C; the derivative of exp(a*x) is a*exp(a*x). When a = 1 these both give just exp(x). For a = 2 they give (1/2) exp(2x) and 2 exp(2x), respectively.

RGV

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DryRun

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thanks villyer, I hadn't thought about that.

The derivative of [itex]e^x[/itex] is: [tex]e^x .\frac{d(x)}{dx}[/tex]

That's exactly what i said before.

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if you're talking about post 4, then i don't think you provided enough info to convey that

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DryRun

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if you're talking about post 4, then i don't think you provided enough info to convey that

It's obvious that [itex]\frac{dx}{dx}=1[/itex] which gives [itex]e^x .1=e^x[/itex]. Unless, you didn't know that, but it's really a basic notion of the principles of differentiation.The derivative of [itex]e^x[/itex] is: [tex]e^x .\frac{d(x)}{dx}[/tex]

You should go over the basic principles, as it should help you to understand ##e^x## and the others more complicated that will follow.

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if it was obvious i would not have posted the question

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if it was obvious i would not have posted the question

d(e

And so

∫e

Note that integration is just reverse of differentiation.

If you want to verify this , then its simple ! Differentiate the left hand side of equation (i) with respect to x and see if its equal to e

If you want to prove it then analyze it by means of graph of f(x)=e

And note if you do this :

d(e

But it can never be xe

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