Help with integration question

I have completed parts 5a_ and 5b) but I am having troubles with answering 5c. I am aware that I need to use integration by parts, but I still do not know how to complete it.

Reply 1

mqb2766

21

Usually with IBP you want to differentiate one of the terms until its a constant and the other term to be easily integrable. Seems fairly clear which is which?

Reply 2

Matheen1

OP

10

Original post by mqb2766

Usually with IBP you want to differentiate one of the terms until its a constant and the other term to be easily integrable. Seems fairly clear which is which?

I chose u=e^-2t and dv/dx=3t. Is that correct??

Reply 3

mqb2766

21

Original post by Matheen1

I chose u=e^-2t and dv/dx=3t. Is that correct??

So why that choice
* 3t can be easily integrated or differentiated. Integrating it makes it a quadratic, cubic, quartic, ...
* e^(-2t) can be easily integrated or differentiated, and its essentially unchanged.

Reply 4

Matheen1

OP

10

Original post by mqb2766

So why that choice
* 3t can be easily integrated or differentiated. Integrating it makes it a quadratic, cubic, quartic, ...
* e^(-2t) can be easily integrated or differentiated, and its essentially unchanged.

So I am correct or wrong?

Reply 5

mqb2766

21

Original post by Matheen1

So I am correct or wrong?

Getting it right or wrong is less important than understanding why you should choose it. But Its wrong. Doing it your way would transform the integrand which is
linear*exponential
into
quadratic*exponential
which is harder. Doing it the other way transforms the integrand into
exponential
which is easy as the derivative of the linear term is simply a constant.

(edited 11 months ago)

Help with integration question

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