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Explain how you would use the power integration formula to integrate the function f(x) = (1/x^2)-(1/x)+(1/4).

  • Calculus - ,

    Integrate each of the three terms separately, using what you call the "power integration formula", and add up the results.

    The formula you are probably refering to is:

    Integral of (a*x^n) = a*n*x^(n+1)/(n+1)

    where a is the constant coefficient and n is the constant exponent.

    1/4 can be thought of as (1/4)*x^0, so its integral is (1/4)*x^1/1 = x/4

    The integral of the 1/x term is a special case, since you cannot divide by zero. Its integral is the natural logarithm of x, ln x

    Now integrate the 1/x^2 term and add the integral results of all three terms. You can add an arbitrary constant at the end if you wish.

    The final answer is

    -1/x + ln x +x/4 + C

  • Calculus - ,

    How do you integrate a radical function such as f(x)= ã(7&4x^5 )- 3ã(6&x^5 )- 11∜x +3∛x ? Describe your strategy.

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