How do you know when to use “integration by parts”?

Published October 25, 2010

Question by dawn treader: How do you know when to use “integration by parts”?
I have a calc test tomorrow, and i want to know that when I see a question, i know what method to use, such as by parts, trig sub. or by partial fraction.

it seems that the hardest one to identify is the one to integrate by parts, can someone give me a hint.

for example, evauluate the integral of (t)sec^2(2t)dt, if i solve this prob. by parts, which term do i assign it as “u” and which one is “dv”?

Best answer:

Answer by Jacy
Whenever, you have a product of two functions: u snd v.

Since;

D(UV) = UdV + VdU

then,

∫UdV = UV – ∫VdU,

Let u = t, a simple independent variable is best to assign u.

while dV = dependent function of u .

So any function nesting will automatically be accounted for
in the derivative.

Consider, evaluating the integral:

∫ t² sin(t) dt,

let u = t, du = dt,

dv = sin t, v = -cos t

∫UdV = UV – ∫VdU,

= t cos t + ∫ cos t dt = t cos t + sin t + C

so, by choosing the independent variable and as it changes
value we determine the effect on the product of functions.

GL2U!

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