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    Ok the question seems pretty simple to find the indefinite integral of sqrt(x^2-6x+5)

    In the answer sheet this is done by substitution of u=x-3 as the expression when completing the square goes to (x-3)^2-4
    (see attached)

    My question is why can't we just use power rule by raising the power to 1/2 then dividing by the derivative of bracket... I don't know if it's too late and my brain isn't working or what.
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    (Original post by Mystery.)
    Ok the question seems pretty simple to find the indefinite integral of sqrt(x^2-6x+5)

    In the answer sheet this is done by substitution of u=x-3 as the expression when completing the square goes to (x-3)^2-4
    (see attached)

    My question is why can't we just use power rule by raising the power to 1/2 then dividing by the derivative of bracket... I don't know if it's too late and my brain isn't working or what.
    The power rule (sometimes called reverse chain rule) only works for integration when the inner function is linear.

    So you could use it for \displaystyle (2x+3)^{\frac{1}{2}} but not for \displaystyle (x^2-6x+5)^{\frac{1}{2}}.

    Try using a substitution u = 2x+3 for the first one and then u = x^2-6x+5 for the second one and see why it doesn't work.
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    (Original post by Notnek)
    The power rule (sometimes called reverse chain rule) only works for integration when the inner function is linear.

    So you could use it for \displaystyle (2x+3)^{\frac{1}{2}} but not for \displaystyle (x^2-6x+5)^{\frac{1}{2}}.

    Try using a substitution u = 2x+3 for the first one and then u = x^2-6x+5 for the second one and see why it doesn't work.
    Thanks!
 
 
 
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