# plz give me the formula of integration by parts

• June 13th 2012, 03:04 AM
cooper607
plz give me the formula of integration by parts
i need to know the integration formula for double components like integration of u*v......plz suggest
• June 13th 2012, 03:42 AM
tom@ballooncalculus
Re: plz give me the formula of integration by parts
Just in case a picture helps...

http://www.ballooncalculus.org/asy/maps/parts.png

... is lazy integration by parts, doing without u and v.

http://www.ballooncalculus.org/asy/prod.png

... is the product rule. Straight continuous lines differentiate downwards (integrate up) with respect to x.

See here.

The formula, of course, (one version, anyway) is

$\int u v'\ dx = uv - \int u' v\ dx$

But the important thing is to see how it depends entirely on working backwards through the product rule for differentiation.

Also: Integration by parts - Wikipedia, the free encyclopedia

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• June 13th 2012, 03:47 AM
biffboy
Re: plz give me the formula of integration by parts
• June 13th 2012, 10:50 PM
richard1234
Re: plz give me the formula of integration by parts
It's pretty easy to derive.

The product rule says that, for two functions u and v in terms of x, $\frac{d}{dx} (uv) = u \frac{dv}{dx} + v \frac{du}{dx}$. Integrate both sides with respect to x to obtain

$uv = \int u \frac{dv}{dx} dx + \int v \frac{du}{dx} dx$

$uv = \int u dv + \int v du$

Rearranging, we get the integration by parts formula, $\int u dv = uv - \int v du$ (you can add an arbitrary constant).
• June 14th 2012, 06:57 AM
Soroban
Re: plz give me the formula of integration by parts
Hello, cooper607!

Quote:

I need to know the formula for integration by parts.

$\text{Formula: }\:\int u\,dv \;=\;uv - \int v\,du$
n . . . . . . . . . . . . . . $\uparrow\qquad\quad\uparrow$
. . . . . . . . . . $\text{"ultra-violet\; voodoo"}$