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HSC 2015 MX2 Integration Marathon (archive) (1 Viewer)

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leehuan

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Re: MX2 2015 Integration Marathon

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Please help...

 

Sy123

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Re: MX2 2015 Integration Marathon

Integrate by parts, letting to get



Integrate by parts again, letting



Notice that the integral now is the same integral originally, so let that equal I, then collect like terms:

 
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photastic

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Re: MX2 2015 Integration Marathon

Integrate by parts, letting to get



Integrate by parts again, letting



Notice that the integral now is the same integral originally, so let that equal I, then collect like terms:

Shouldn't the answer be

 

Ekman

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Re: MX2 2015 Integration Marathon

Next Question:



Edit: Try doing it without using t-method
 
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Ekman

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Re: MX2 2015 Integration Marathon

Here's a better one:

 

Ekman

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Re: MX2 2015 Integration Marathon

How did you get those expressions for the integral in the first line ?
And so the tan at the top will cancel with the denominator. For converting it into the sin and cos fraction, just make the tan^2x in the denominator into sin^2x/cos^2x, then just simplify
 
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