Calculus 2
posted by Heather .
find the integral of x/(x^2+4)dx using trigonometric substitution.

Calculus 2 
Reiny
I don't understand why you were instructed to use trig substitution for this question, it is straightforward
You should recognize certain pattern of derivatives and integrals
Notice that the derivative of the denominator is 2x and we have x at the top, so this follows the pattern of log derivatives directly
If we had ∫2x/(x^2 + 4) dx it would simply be ln(x^2 + 4) + c
so for
∫ x/(x^2+4) dx we would get (1/2) ln(x^2 + 4) + c 
Calculus 2 
Heather
we are supossed to do it both ways. i got it using the usubstitution method. we are supossed to show that the answers are equivalent.
Respond to this Question
Similar Questions

Calculus
I have two questions, because I'm preparing for a math test on monday. 1. Use the fundamental theorem of calculus to find the derivative: (d/dt) the integral over [0, cos t] of (3/5(u^2))du I have a feeling I will be able to find … 
Calculus
For the following integral find an appropriate trigonometric substitution of the form x=f(t) to simplify the integral. INT((4x^23)^1.5) dx x=? 
Calculus
For the following integral find an appropriate TRIGONOMETRIC SUBSTITUTION of the form x=f(t) to simplify the integral. INT (x^2)/(sqrt(7x^2+4))dx dx x=? 
Calculus
For the following integral find an appropriate TRIGONOMETRIC SUBSTITUTION of the form x=f(t) to simplify the integral. INT x(sqrt(8x^264x+120))dx x=? 
Calculus
For the following integral find an appropriate TRIGONOMETRIC SUBSTITUTION of the form x=f(t) to simplify the integral. INT (x)/(sqrt(1918x^2+80x))dx x=? 
calculus
For trigonometric substitution to solve the above integral, fill in the blanks below using the picture of the triangle given. integral (x^3)/(sqrt(25+9x^2)) dx / l / l / l / l / l / l / l / l / l side A / l / l  side B *** … 
Calculus 2
Evalute the integral of x/(x^2+4)dx using usubstitution and then trigonometric substitution. I did this and got (1/2)ln(x^2+4)+C using usubstitution and x^2+4+C using trigonometric substitution. What did I do wrong? 
Calculus II
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? 
Math
(i) Evaluate integral [ x^3 / (x^2 + 4)^2 ] using trigonometric substitution. (ii) Evaluate integral [ x^3 / (x^2 + 4)^2 ] using regular substitution. (iii) Use a right triangle to check that indeed both answers you obtained in parts … 
Question on Integration
(i) Evaluate integral [ x^3 / (x^2 + 4)^2 ] using trigonometric substitution. (ii) Evaluate integral [ x^3 / (x^2 + 4)^2 ] using regular substitution. (iii) Use a right triangle to check that indeed both answers you obtained in parts …