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    I'm stuck on a couple of what i think should be quite simple integration questions so i would really appreciate some help!

    First one is: integrate (2x-1) / sqrt x

    and the second: integrate cosec^2 (3x+4)

    any help at all would be greatly appreciated, cheers
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    first one: (2x-1)/sqrt x =

    (2x-1)x^-1/2=

    2x^1/2 -x^-1/2

    integrate from here.
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    ............
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    2x-1/sqrt x = (2x-1)(x ^-1/2)
    =(x^2 - x)(2x^1/2)+C

    i think
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     \int \frac{2x-1}{\sqrt x}
    = \int (2x-1)x^{-\frac{1}{2}}
    = \int x^{\frac{1}{2}} - x^{\frac{-1}{2}}
    Which is basic C2 integration.

    I'm still looking at the 2nd
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    For the second one, I think you have to solve the cosec^2=1/sin2x and then intergrate that and then use the product rule to solve the whole thing. Or maybe the direct substitution or intergrating by substitution. I might come back and tell you once I've solved it. But I have to go out for a bit might reurn to you in abit//
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    I've done it use the substitution.
    integral cosec^2(4+3 x) dx
    substitute u = 3 x+4 and du = 3
    dx: = 1/3 integral cosec^2(u) du
    The integral of cosec^2(u) is -cot(u):
    = -(cot(u))/3+c
    Substitute back for u = 3 x+4:
    = -1/3 cot(3 x+4)+c
 
 
 
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Updated: January 18, 2010
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