- #1

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i just started learning Integration last week so not exactly sure how to approch this type of question.

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- Thread starter gona
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- #1

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i just started learning Integration last week so not exactly sure how to approch this type of question.

- #2

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Do you know how to integrate 1/sinx?

- #3

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no this is the first time i have seen where a trigonometric function is on the denominator

but now that i think about it

sinx = [tex]\sqrt{1-cos^2x}[/tex]

and arcsin was equal to [tex]\frac{1}{((1-x^2)}[/tex]

so i guess i could use the U substituition method

and then the answer would be...arcsin(cosx)??? im not too sure

but now that i think about it

sinx = [tex]\sqrt{1-cos^2x}[/tex]

and arcsin was equal to [tex]\frac{1}{((1-x^2)}[/tex]

so i guess i could use the U substituition method

and then the answer would be...arcsin(cosx)??? im not too sure

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- #4

Dick

Science Advisor

Homework Helper

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No, no arcsin. But you might want to try multiplying numerator and denominator by (1-sin(x)). It may look more familiar.

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- #5

daniel_i_l

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You could also try the subsitution u = tan(x/2). It looks a little messy but everything cancels out.

- #6

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sinx = [tex]\frac{2tan(\frac{x}{2})}{1+tan^{2}(\frac{x}{2})}[/tex]

soo then i symplify the equation so that it is

[tex]\frac{1+tan^{2}(\frac{x}{2})}{1+tan^{2}(\frac{x}{2})+2tan(\frac{x}{2})}[/tex]

the i used u = tan[tex](\frac{x}{2})[/tex]

so i get [tex]\frac{1+u^{2}}{(u+1)^{2}}[/tex]

What should i do from here or is this the right way at all?

- #7

Dick

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- #8

daniel_i_l

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1/(1+cosx+sinx) the substitution u=tan(x/2) is good.

But notice that it isn't x = tan(u/2) but rather u=tan(x/2). In order to get this into something the the example I gave you can show with so trig identities that if u=tan(x/2) then:

dx = 2du/(1+u^2)

sinx = 2u/(1+u^2)

cosx = (1-u^2)/(1+u^2)

If you substitue all that you the (1+u^2)s candel out and you get some rational function which you can solve with the typical rational function method (breaking it into elementry functions...)

- #9

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the answe was tanx - secx +c

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