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Math Help - A simple problem

  1. #1
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    A simple problem

    Hi folks, I stumbled on this forum in Google and it looks like a really lively and well-mainted help forum. I'm currently doing Calculus II in CEGEP and need quite a bit of help. I've been laying it off for so long and I'm so behind, but I need to start getting things together and catch up.

    I'll start with a homework problem, I know you guys have a math code here (which is awesome) I'm not entirely used to it yet, so I've just posted and img of my problem (a rather simple one, but I just don't know where to begin):



    We've been studying substitution method and integration by parts, I barely have a grasp on those concepts. If someone can go through this problem and lay things out for me in layman's terms, it would really help me in my first few steps.

    I look forward to being a part of this forum. Mathematics is definitely something I want to drastically improve in.

    Thanks/Cheers
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Merkw‹rdigeliebe View Post
    Hi folks, I stumbled on this forum in Google and it looks like a really lively and well-mainted help forum. I'm currently doing Calculus II in CEGEP and need quite a bit of help. I've been laying it off for so long and I'm so behind, but I need to start getting things together and catch up.

    I'll start with a homework problem, I know you guys have a math code here (which is awesome) I'm not entirely used to it yet, so I've just posted and img of my problem (a rather simple one, but I just don't know where to begin):



    We've been studying substitution method and integration by parts, I barely have a grasp on those concepts. If someone can go through this problem and lay things out for me in layman's terms, it would really help me in my first few steps.

    I look forward to being a part of this forum. Mathematics is definitely something I want to drastically improve in.

    Thanks/Cheers
    integration by parts should work. let u = x and dv = \tan^2 x

    those are the variables usually used in the formula
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  3. #3
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    dv=\tan^2x\,dx of course.
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  4. #4
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    thanks for the help, I don't think you guys realize that I'm incredibly oblivious to these concepts, at this point I merely repeating/following patterns, I don't actually understand what I'm doing

    I followed a step by step example from Wikipedia and finished off with

    x(tan^2)x + 2ln|cosx| + C


    is that right?
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  5. #5
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Krizalid View Post
    dv=\tan^2x\,dx of course.
    but of course, i did that to mess with you and Mr Fantastic
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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Merkw‹rdigeliebe View Post
    thanks for the help, I don't think you guys realize that I'm incredibly oblivious to these concepts, at this point I merely repeating/following patterns, I don't actually understand what I'm doing

    I followed a step by step example from Wikipedia and finished off with

    x(tan^2)x + 2ln|cosx| + C


    is that right?
    um, i don't think so.

    remember the formula (if you use it, i don't):

    \int u~dv = uv - \int v~du

    so that means, \int x \tan^2 x ~dx = x \left( \int \tan^2 x~dx \right) - \int 1 \cdot \left( \int \tan^2 x ~dx \right)~dx


    so, now figure out what is \int \tan^2 x~dx and plug it in


    we dealt with that integral here
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  7. #7
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    so my answer should be -2xln|cosx| + 2ln|cosx| + C
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  8. #8
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    I believe it's x(tan x - x) + ln|cos x| + 1/2 x^2 + c
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  9. #9
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    Yeah, this is what I ended up getting:



    + C of course...


    thanks for all your help guys
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