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Math Help - Integrate

  1. #1
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    Integrate

    I am stuck on these three problems because I didn't understand how the teacher was teaching it. The test is in two days.

    1.∫(x^3-2x+2)dx

    2.∫(sqrt(x) - 1/x^2)dx

    3.∫(2x^3+1)^2 x^2 dx

    Thanks for the help.
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by uniquereason81 View Post
    I am stuck on these three problems because I didn't understand how the teacher was teaching it. The test is in two days.

    1.∫(x^3-2x+2)dx

    2.∫(sqrt(x) - 1/x^2)dx

    3.∫(2x^3+1)^2 x^2 dx

    Thanks for the help.
    1. \int{x^3-2x+3}dx=\frac{x^4}{4}-x^2+2x+C...you do this by basic integration technique...
    2. \int{\sqrt{x}-\frac{1}{x^2}dx}=\int{x^{\frac{1}{2}}-x^{-2}dx}=\frac{2x^{\frac{3}{2}}}{3}+\frac{1}{x}+C
    3. \int{(2x^3+1)^2\cdot{x^2}}dx=\frac{1}{6}\int{6x^2\  cdot(2x^3+1)^2dx}=\frac{(2x^3+1)^3}{18}+C
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  3. #3
    MHF Contributor Mathstud28's Avatar
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    Just so you know

    Quote Originally Posted by Mathstud28 View Post
    1. \int{x^3-2x+3}dx=\frac{x^4}{4}-x^2+2x+C...you do this by basic integration technique...
    2. \int{\sqrt{x}-\frac{1}{x^2}dx}=\int{x^{\frac{1}{2}}-x^{-2}dx}=\frac{2x^{\frac{3}{2}}}{3}+\frac{1}{x}+C
    3. \int{(2x^3+1)^2\cdot{x^2}}dx=\frac{1}{6}\int{6x^2\  cdot(2x^3+1)^2dx}=\frac{(2x^3+1)^3}{18}+C
    the second one I just converted the variables to a more hospitable form and applied general integration technique..

    the second one I just made it so it was an example of \int{f(g(x))\cdot{g'(x)}}dx after doing this I could integrate f(g(x)) as though it was just f(x)...so by making the derivative of the inside on the outside I could integrate (2x^3+1)^2 as though it was just x^2 and get x^3 and then you substitute back in the g(x)
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  4. #4
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    wow i wish you could be my math teacher
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  5. #5
    MHF Contributor Mathstud28's Avatar
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    Haha

    Quote Originally Posted by uniquereason81 View Post
    wow i wish you could be my math teacher
    Considering I am only in eleventh grade I dont think thats going to happen..but anytime you need help...Im here!
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  6. #6
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    LOL you should think about teaching as a side job. Making some big bucks.
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  7. #7
    MHF Contributor Mathstud28's Avatar
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    Haha

    Quote Originally Posted by uniquereason81 View Post
    LOL you should think about teaching as a side job. Making some big bucks.
    Someday my friend...maybe I'll be your kid's college professor
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  8. #8
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    Hey man these three are giving me problems

    1) ∫(2x^3 + )^2 x*dx

    2) ∫x*sqrt(2x^3 + 1) dx

    3) ∫ (x + 1)dx/cube root(x^2 + 2x -2)

    Number 3 is the most confusing to me.
    THANKS
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  9. #9
    MHF Contributor Mathstud28's Avatar
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    Next time start a new thread

    Quote Originally Posted by uniquereason81 View Post
    Hey man these three are giving me problems

    1) ∫(2x^3 + )^2 x*dx

    2) ∫x*sqrt(2x^3 + 1) dx

    3) ∫ (x + 1)dx/cube root(x^2 + 2x -2)

    Number 3 is the most confusing to me.
    THANKS
    You need to rewrite these....they dont make sense..
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  10. #10
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    oops sorry.

    1) ∫(2x^3 + 1)^2 * x * dx

    2) ∫ x square root (2x^3 + 1 ) dx

    3) ∫ (x +1 ) dx over cube root of (x^2 + 2x -2)

    i don't know how to symbols
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  11. #11
    MHF Contributor Mathstud28's Avatar
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    IT is ok

    Quote Originally Posted by uniquereason81 View Post
    oops sorry.

    1) ∫(2x^3 + 1)^2 * x * dx

    2) ∫ x square root (2x^3 + 1 ) dx

    3) ∫ (x +1 ) dx over cube root of (x^2 + 2x -2)

    i don't know how to symbols

    http://www.mathhelpforum.com/math-he...-tutorial.html first of all that will teach you how to use LaTeX and be better understood...now on to the integrals \int{(2x^3+1)^2\cdot{x}dx}...for this one honestly I would jsut distribute and integrate...or use the method I will show you on the others

    2) \int{x\sqrt{2x^3+1}dx}..for this you must make a u-substitution..so you say that u=\sqrt{2x^3+1}...then say that \sqrt[{3}]{\frac{u^2-1}{2}}=x..and finally then you have that dx=\frac{\sqrt[{3}]{4}u}{2(u^2-1)^{\frac{2}{3}}}..and now you can see that this has no means that you could use to find the integral...there are ways but trust me for your level you must have copied it down wrong

    3)Ok for this one we have \int{(x+1)\cdot[x^2+2x-2}]^{\frac{-1}{3}}dx}which I wont do for you but I will give you a hint \frac{1}{2}\int{(2x+2)\cdot[x^2+2x-2]^{\frac{-1}{3}}dx}
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  12. #12
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    I got this stuff down pact. And thanks for the website.
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  13. #13
    MHF Contributor Mathstud28's Avatar
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    Hey

    Quote Originally Posted by uniquereason81 View Post
    I got this stuff down pact. And thanks for the website.
    No problem anytime
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