integration by different parts

Identity · 2009-12-14 23:31:16

Let

There are 4 ways to do this by integration by parts, are they equivalent?

and... i could go on and do

dv = e^{3x}dx, u = e^{3x}

dv = e^{3x}dx, dv = e^{3x}dx

But too much algebra and my head hurts

Anyway, why do they give different answers??

Last edited by Identity (2009-12-14 23:32:26)

Avon · 2009-12-15 08:57:15

You have made a mistake in the second one.

If

then

If you correct this you will show that

soroban · 2009-12-15 09:42:19

. .

. . . . . .

. . . . . . . . . .

. . . . . . . . . . . .

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

.

Identity · 2009-12-15 14:33:58

Thanks so much soroban and avon! I shouldn't do maths too late at night

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