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Math Help - integration problems - urgent

  1. #1
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    Question integration problems - urgent

    Hi,

    Attached document contain question rearding indefinite integrals.

    Can someone help to provide solution for all three questions ASAP.

    Apologise for improper way of defining the question as i don't have the software in which we can draw maths problem nicely.

    Thanks in advance.

    Best Regards,
    Lalit Chugh[B]
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  2. #2
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    1. \int \frac{\tan(x)}{\cot(x)}dx

    1/cot(x) is simply tan(x), so this integral is really \int \tan^2(x)dx

    Use this identity and it should be easy.

    1+\tan^2(x)=\sec^2(x)
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  3. #3
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    2. \int \sqrt{x}\left(x^5+\frac{3}{x}\right)dx

    Just distribute the square root of x and use basic power rules.

    \int x^{5+\frac{1}{2}}+\frac{3}{x}*x^{\frac{1}{2}}dx
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  4. #4
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    Quote Originally Posted by Jameson
    1. \int \frac{\tan(x)}{\cot(x)}dx

    1/cot(x) is simply tan(x), so this integral is really \int \tan^2(x)dx

    Use this identity and it should be easy.

    1+\tan^2(x)=\sec^2(x)
    _____________

    for this problem, i think just rewrite the function in term tanx = sinx/cosx
    then, you will flip cosx into the denominator. It will come out like this, intergal of (sinx/cos^2x)dx
    next step, using the sub methods

    let u = cosx, du = - sinxdx

    -du = sinxdx

    then just jam that into the integral.

    u will get something like du/u^2

    bring u^2 on top : u-2

    take the integral. u^-1/-1 or

    1/-cosx + c will become your answer
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  5. #5
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    Quote Originally Posted by distance
    _____________

    for this problem, i think just rewrite the function in term tanx = sinx/cosx
    then, you will flip cosx into the denominator. It will come out like this, intergal of (sinx/cos^2x)dx
    next step, using the sub methods

    let u = cosx, du = - sinxdx

    -du = sinxdx

    then just jam that into the integral.

    u will get something like du/u^2

    bring u^2 on top : u-2

    take the integral. u^-1/-1 or

    1/-cosx + c will become your answer
    i think the answer is tanx - x + c
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  6. #6
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    i agree with you.

    Answer comes to: tanx - x + c
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  7. #7
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    Yes. This is the correct answer. Using the substitution I gave you get \int \sec^2(x)-1dx. And thus the answer follows.
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