Posted by Bill on Monday, January 12, 2009 at 7:58pm.
find the integral of x^2  sec3xtan3x

Calculus  Damon, Monday, January 12, 2009 at 8:28pm
well spit it into 2 integrals
integral x^2 dx = x^3/3
sec^3 x tan x^3 dx
= (1/cos^3)(sin^3/cos^3) dx
=sin^3/cos^6 dx
I can give you a recursion formula for this
int dx sin ^m x/cos^n = sin^(m+1) x/[(n1)cos^(n1)x]  [(mn+2)/(n1)] int dx sin^m x/ cos^(n2) x
do that until you get to sin^3 x
now int dx sin^3 x is cos x + (1/3) cos^3 x

Calculus  Reiny, Monday, January 12, 2009 at 11:21pm
or if you really meant
sec(3x)tan(3x)
the derivative of secx
= (secx)tanx
so the integral of sec3xtan3x = (1/3)sec3x
so the integral of
x^2  sec3xtan3x
is
(1/3)x^3  (1/3)sec3x + C
You have to be careful how you type these, as you can see they can be interpreted in different ways unless you use brackets to clearly state what you want.
Answer This Question
Related Questions
 calculus  LEt f and g be continous functions with the following properties i. g...
 calculus  LEt f and g be continous functions with the following properties i. g...
 Calculus  Find the volume of the solid whose base is the region in the xyplane...
 Calculus II/III  A. Find the integral of the following function. Integral of (x...
 Calculus  If f(x) and g(x) are continuous on [a, b], which one of the following...
 Calculus  Integrals  I have 3 questions, and I cannot find method that ...
 Calculus  Integrals  I have 3 questions, and I cannot find method that ...
 Math/Calculus  How would I solve the following integral with the substitution ...
 Calculus II  Integrate using integration by parts (integral) (5x) e^3x u = 5x...
 Calculus: Integral  I don't understand how to do this one integral problem that...
More Related Questions