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I'm having trouble finding the integral using usubstitution. 
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#1
Jun811, 01:57 PM

P: 19

1. The problem statement, all variables and given/known data
I have to integrate using usubstitution (probably). Ex. 1 Integrate (sin^4x)/(cos^6x)dx 2. Integrate (2x)/(sqrt(e^(2x^2)1))dx 3. Integrate (cos^1x)/(sqrt(1x^2))dx Thank you ! 2. Relevant equations I do not want the solutions. I just need to be pointed in the right direction (i.e. I need you to help me start off) **It should be noted that I am doing a calculus II course (Integral Calc, mostly) in university, so it's not very advanced integrals that I'm doing. Basically what I know is how to integrate using usubstitution, and I know the integrals for the inverse trig functions (which is supposed to be relevant to examples 2 & 3), and that's what information I have to work with. **It should also be noted that I may just not know how to rewrite the equations before I can integrate them. I have trouble 'seeing through' the equation and automatically knowing which way I'm going to solve it. 3. The attempt at a solution Ex. 1 I tried rewriting the equation using trig identities, e.g. (1cos(x))/(1sin(x))^3. I found this got me nowhere. I also tried rewriting it is (sin^4)(x)/(cos^4)(x)*1/cos(x), and rewriting and rewriting until I ended up with a big mess, so that got me nowhere as well. 2. Here's my dilemma: if I substitute e^2x for u, I end up needing an e to the power in my numerator, so that doesn't work out. if I instead substitute 2x^2 for u, I end up with the e to the power of u on the bottom and I don't have a formula for that. 3. I have no ideas on this one. 


#2
Jun811, 02:07 PM

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BTW, welcome to Physics Forums! 


#3
Jun811, 03:42 PM

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PF Gold
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For example 2, rewrite the integrand to remove the sqrt in the denominator, that is, express 1/sqrt(e^(2*x^2)1) using the appropriate exponent. After doing this, see if the factor 2x would be useful in integration by parts.



#4
Jun811, 03:44 PM

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PF Gold
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I'm having trouble finding the integral using usubstitution.
See if the factor 2x would be useful in a usubstitution integration. 


#5
Jun811, 05:43 PM

P: 19

Thanks all, but I still cannot find the solution to the second example.
I let u=2x, so du=2dx Since the x is is still in the numerator, I say that also, x=u/2 So I fill this in and I get Integral of (u/2)(1/(sqrt((e^u)1))du I have not yet learned to do integration by parts, by the way. 


#6
Jun811, 06:06 PM

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PF Gold
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The argument of the exponential has an x^{2} in it, right? So try u=x^{2} to try simplify that a bit. That's where you find the factor of 2x comes in handy.
Then you might try a substitution like v=e^{u} and see where that gets you. A lot of this you figure out by trial and error. As you do more problems, you'll start to get a feel for what works and what doesn't. 


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