Calculus
posted by Nikki .
int(dx/(x^2+9)) u = x/3
Use the indicated substitution (above) to evaluate the integral. Confirm answer by differentiation.
Okay, so I found that du/dx is 1/3. dx is 3du. Just by looking at the integral I can tell this is some form of tan^1(x), if we change it to int(1/(x^2+9) * dx). Thing is, I don't really know where to put in u to make this work. Help please???
Thank you!

u=x/3
du = (1/3)dx
dx = 3du
x²=9u²
Substitute in the integral to get:
∫ dx/(x²+9)
=∫ 3du/(9u²+9)
=∫ (1/3)du/(x²+1)
Can you take it from here, using your tan^{1} suggestion?
Respond to this Question
Similar Questions

Calculus
Hello, I have some calculus homework that I can't seem to get started..at least not on the right track? 
calculus please help
what is the integral of x/(1+x^2)^2 dx This is a question of a past AP exam of calculus BC i know i have to use the substitution method where u=(1+x^2), du=2xdx. I have to find the integral but i'm just focused on the coefficient because … 
calc
how do you start this problem: integral of xe^(2x) There are two ways: 1) Integration by parts. 2) Differentiation w.r.t. a suitably chosen parameter. Lets do 1) first. This is the "standard method", but it is often more tedious than … 
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 TRIGNOMETRIC SUBSTITUTION of the form x=f(t) to simplify the integral. INT((4x^23)^1.5) dx x=? 
calculus
consider the function f(x) = e^x(sinNx) on the interval [0,1] where N is a positive integer. a) Compute the integral from 0 to 1 of f(x). Evaluate this integral when N=5, N=10, and N=100. B) What happens to the graph and to the value … 
calculus
consider the function f(x) = e^x(sinNx) on the interval [0,1] where N is a positive integer. a) Compute the integral from 0 to 1 of f(x). Evaluate this integral when N=5, N=10, and N=100. B) What happens to the graph and to the value … 
calculus
Use the indicated substitution to evaluate the integral integral 18sec(2x) tan(2x)dx, u=2x 
Calculus Please Help2
Evaluate the integral by using substitution. Use an uppercase "C" for the constant of integration. integral x^5((x^62)^10)dx ty