Need help with an integral

[PowerMacG5]

The integral is
int(1/(1-sin(x))dx

I tried letting u equal 1-sinx but that got me no where. I tried integration by parts, but I have no idea what to let u and dv equal to. Any help is appreciated.

 

[TranSoft]

trig identities

 

[PowerMacG5]

Originally posted by: TranSoft
trig identities

Would you like to elababorate more? Else, bump.

 

[PowerMacG5]

Bump

 

[dullard]

int(1/(1+-sin(ax))dx = -+ (1/a) tan(pi/4 -+ ax/2)

In your case: a=1 and use the + or - sign listed second. Thus your answer is:

int(1/1-sin(x))dx = + tan (pi/4 + x/2)

That is something that most teachers force beginning calculus students to memorize as the definition of the derivitive of the tangent function. However you should be able to work it out.

 

[PowerMacG5]

Originally posted by: dullard
int(1/(1+-sin(ax))dx = -+ (1/a) tan(pi/4 -+ ax/2)

In your case: a=1 and use the + or - sign listed second. Thus your answer is:

int(1/1-sin(x))dx = + tan (pi/4 + x/2)

That is something that most teachers force beginning calculus students to memorize as the definition of the derivitive of the tangent function. However you should be able to work it out.

I have never once seen that before in my life. Can you explain why it works or not? I would like to be able to show steps, rather than arbitrarily stating something as fact. Are there any substitutions, change of variables, integration by parts, etc...?

 

[jmcoreymv]

My Ti 89 says its -cos(x) / (sin(x) - 1)

 

[PowerMacG5]

Originally posted by: jmcoreymv
My Ti 89 says its -cos(x) / (sin(x) - 1)

So does mine, but that doesn't help me. I would like to know why. Also maple gives a different answer, but they differ by a constant, so they are both valid. I would like to see the steps needed, and what to do. Anyone can mindlessly enter numbers into a calculator and write the answer down, I would like to see why the calculator spits said numbers out.

 

[Dissipate]

Originally posted by: Marauder911

Originally posted by: jmcoreymv
My Ti 89 says its -cos(x) / (sin(x) - 1)

So does mine, but that doesn't help me. I would like to know why. Also maple gives a different answer, but they differ by a constant, so they are both valid. I would like to see the steps needed, and what to do. Anyone can mindlessly enter numbers into a calculator and write the answer down, I would like to see why the calculator spits said numbers out.

http://www.calc101.com/

 

[josphII]

multiply the top and bottom by 1+sin(x) ?

 

[PowerMacG5]

Originally posted by: Dissipate

Originally posted by: Marauder911

Originally posted by: jmcoreymv
My Ti 89 says its -cos(x) / (sin(x) - 1)

So does mine, but that doesn't help me. I would like to know why. Also maple gives a different answer, but they differ by a constant, so they are both valid. I would like to see the steps needed, and what to do. Anyone can mindlessly enter numbers into a calculator and write the answer down, I would like to see why the calculator spits said numbers out.

http://www.calc101.com/

Alright. So that gives me the answer and steps, but I have no idea why it does something. Can someone tell me why it makes the subsitution u = tan(x/2)? It then goes into a sequence of events which I do not understand.

 

[PowerMacG5]

Bump

 

[JetBlack69]

Originally posted by: josphII
multiply the top and bottom by 1+sin(x) ?

that's my thinking too, then you have

int( (1+sin(x))/(cos(x)^2)) then you have

int (1/cos(x)^2) + int (sin(x)/(cosx)^2)

 

[PowerMacG5]

Originally posted by: josphII
multiply the top and bottom by 1+sin(x) ?

I must have missed your post when reading through the thread. Wow, thanks for the help. It works like a charm. Sometimes the simplest solutions can elude you. I thank you again.