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    Hi,

    I'm struggling with some integration questions as I'm not sure which method to use or I've started and then got really stuck. Any advice would be really appreciated.

    Thanks
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    (Original post by VioletPhillippo)
    Hi,

    I'm struggling with some integration questions as I'm not sure which method to use or I've started and then got really stuck. Any advice would be really appreciated.

    Thanks
    Recall that \displaystyle\int f'(x)G(f(x)) \ dx = \displaystyle\int G(u) \ du. To see this, make the sub u=f(x), this forms a sort of reverse chain rule.

    You can apply this reasoning to each of the questions, though in some it may be easier to recall the special case of the above:
    \displaystyle\int \dfrac{f'(x)}{f(x)} \ dx = \ln(f(x)) \ (+ \ \mathcal{C}).
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    (Original post by VioletPhillippo)
    Hi,

    I'm struggling with some integration questions as I'm not sure which method to use or I've started and then got really stuck. Any advice would be really appreciated.

    Thanks
    1 - Use u=x^2-1

    2 - Top is differential of the bottom, I assume you know what to do here

    3 - Top is the differential of the bottom.

    4 - Use u=\sin(x)
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    you can use "changing the variable" in all of these questions...

    i) new variable = x2 - 1

    ii) new variable = ex

    iii) new variable = sinx + 1

    iv) new variable = sinx
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    (Original post by VioletPhillippo)
    Hi,

    I'm struggling with some integration questions as I'm not sure which method to use or I've started and then got really stuck. Any advice would be really appreciated.

    Thanks
    For the first and fourth, the way you know how to choose the substitution is to make u equal the inside of the bracket (or what is in effect a bracket).

    In the fourth one, sin^2 x is the same as (sin x)^2 so the inside of the bracket is sin x.
 
 
 
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