Posted by Katie on Sunday, December 30, 2012 at 7:27pm.
Find x and dx using trigonometric substitution of
(integral) square root of 4x^2  9 divide by x
x = 2/3 sec x
dx = 2/3 tan x dx
Is this right so far?

Calculus II  Steve, Sunday, December 30, 2012 at 7:34pm
∫√(4x^29) dx
2x = 3secθ, so
4x^29 = 9sec^2θ9 = 9tan^2θ
x = 2/3 secθ, so
dx = 2/3 secθ tanθ
and you integral becomes
∫3tanθ (2/3 secθ tanθ) dθ
= 2∫secθ tan^2θ dθ
= 2∫(sec^3θ  secθ) dθ
use integration by parts twice for sec^3θ.

Calculus II  oops  Steve, Sunday, December 30, 2012 at 7:36pm
rats. x = 3/2 secθ, so adjust the constant in the following steps.
when you're all done, you can check your answer by typing in the integral at wolframalpha.com

Calculus II  Katie, Sunday, December 30, 2012 at 7:55pm
ok thank you very much. Happy New Year
Answer This Question
Related Questions
 Calculus  Integration  Hello! I really don't think I am understanding my calc ...
 calculus trigonometric substitution  ∫ dx/ (x^2+9)^2 dx set x = 3tan u dx...
 Calculus 2  Evalute the integral of x/(x^2+4)dx using usubstitution and then ...
 math  How do I derive the secant reduction rule? Integral (sec x)^n dx = ...
 calculus (check my work please)  Not sure if it is right, I have check with the...
 calculus  Use integration by parts to evaluate the integral of x*sec^2(3x). My ...
 calculus  Calculate definite integral of dx/(x^4 * sqrt(x^2 + 3)) Over (1,3) I ...
 Calculus AP  I'm doing trigonometric integrals i wanted to know im doing step ...
 Calculus 2  ∫ tan^2 (x) sec^4 (x) dx ∫ [tan^2 (t) + tan^4 (t)] dt...
 Calculus 2  find the integral of x/(x^2+4)dx using trigonometric substitution.
More Related Questions