Posted by **Mai** on Sunday, May 22, 2011 at 10:22pm.

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

- Calculus -
**drwls**, Monday, May 23, 2011 at 3:44am
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 -
**help**, Saturday, February 4, 2012 at 6:41am
How do you integrate a radical function such as f(x)= (7&4x^5 )- 3(6&x^5 )- 11∜x +3∛x ? Describe your strategy.

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