Posted by **mathstudent** on Monday, December 31, 2007 at 11:54am.

Calculate definite integral of

dx/(x^4 * sqrt(x^2 + 3))

Over (1,3)

I start with the substitution x = sqrt(3)*tan t

so:

sqrt(x^2 + 3) = sqrt(3) * sec t

dx = sqrt(3) * sec^2 t dt

x^4 = 9 * tan^4 t

The integral simplifies to:

= dt/(tan^3 t * sin t)

How do I solve that?

- calculus -
**Damon**, Monday, December 31, 2007 at 2:07pm
Well, I call it:

(1/9)int cos^3 t dt/sin^4 t

(1/9) int (1-sin^2 t) cos t dt/sin^4 t

(1/9) int cos t dt/sin^4 t -(1/9) int cos t dt/sin^2 t

now integral of cos/sin^4 is of form 1/sin^3 (leaving the constants for you

and)

integral of cos/sin^2 is of form 1/sin (leaving the constants to you)

- calculus -
**mathstudent**, Monday, December 31, 2007 at 3:03pm
thanks damon! I follow perfectly.

## Answer this Question

## Related Questions

- calculus - Integrate: dx/sqrt(x^2-9) Answer: ln(x + sqrt(x^2 - 9)) + C I'm ...
- Calculus - Calc length of arc of y=ln(x) from x=1 to x=2 ---- So far: Definite ...
- Math Help please!! - Could someone show me how to solve these problems step by ...
- ap calculus - Which of the following definite integrals gives the length of y = ...
- Calculus - Evaluate the indefinite integral: 8x-x^2. I got this but I the ...
- Mathematics - sqrt 6 * sqrt 8 also sqrt 7 * sqrt 5 6.92820323 and 5.916079783 So...
- Math(Roots) - sqrt(24) *I don't really get this stuff.Can somebody please help ...
- Trig - Find the exact values of the six trigonometric functions 0 if the ...
- Calculus - Please look at my work below: Solve the initial-value problem. y'' + ...
- math calculus please help! - l = lim as x approaches 0 of x/(the square root of...