Wednesday

July 30, 2014

July 30, 2014

Posted by **APpreciative student** on Tuesday, November 23, 2010 at 1:48am.

I'm not sure what the answer to this is; how do I solve?

Find antiderivative of

(1/(x^2))[sec(1/x)][tan(1/x)]dx

I did integration by parts and got to

(1/(x^2))[sec(1/x)] + 2*[antiderivative of (1/(x^3))(sec(1/x))dx]

- AP Calculus BC -
**MathMate**, Tuesday, November 23, 2010 at 7:51amIntegration by parts is the same as any other tool. It's just a tool. You can go around in circles with it... unless you know where you're going.

For this particular problem, I propose to use another tool, substitution.

Did you notice there is the factor (1/x²) at the beginning? What would ∫(1/x²)dx give? ∫-d(1/x).

So the integral becomes:

I=∫(1/(x^2))[sec(1/x)][tan(1/x)]dx

=∫[sec(1/x)][tan(1/x)]d(1/x)

=∫sec(y)tan(y)dy

= ... +C

Do remember, however, if and when you have to evaluate a definite integral, the limits have to correspond to the integration variable, which in this case is (1/x).

**Related Questions**

Integration - Intergrate ¡ì sec^3(x) dx could anybody please check this answer. ...

calculus (check my work please) - Not sure if it is right, I have check with the...

Calculus - could anybody please explain how sec x tan x - ¡ì sec x tan^2(x) dx...

Calculus 12th grade (double check my work please) - 2- given the curve is ...

calculus - find dy/dx y=ln (secx + tanx) Let u= secx + tan x dy/dx= 1/u * du/dx ...

Calculus AP - I'm doing trigonometric integrals i wanted to know im doing step ...

calculus - So I am suppose to evaulate this problem y=tan^4(2x) and I am ...

calculus - Use integration by parts to evaluate the integral of x*sec^2(3x). My ...

Calculus - Integration - Hello! I really don't think I am understanding my calc ...

calculus - Integrate: dx/sqrt(x^2-9) Answer: ln(x + sqrt(x^2 - 9)) + C I'm ...