- #1
paralian
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[SOLVED] Integral with trig substitution
Find [tex]\int(x^3)/\sqrt{x^2-9}[/tex]
Trig substitution. sin^2 + cos^2 =1, and other things that you can figure out from that.
Half angle formula, cos^2[tex]\theta[/tex]=(1+cos(2[tex]\theta[/tex]) )*.5
Let x=3*sec[tex]\theta[/tex]
so dx=3*sec[tex]\theta[/tex]*tan[tex]\theta[/tex] d[tex]\theta[/tex]
When I substitute that in and simplify it, I got:
27*[tex]\int(sec^4(\theta) d\theta)[/tex]
And I don't know how to integrate that. Half angle formulas aren't seeming to work.
Thanks!
Homework Statement
Find [tex]\int(x^3)/\sqrt{x^2-9}[/tex]
Homework Equations
Trig substitution. sin^2 + cos^2 =1, and other things that you can figure out from that.
Half angle formula, cos^2[tex]\theta[/tex]=(1+cos(2[tex]\theta[/tex]) )*.5
The Attempt at a Solution
Let x=3*sec[tex]\theta[/tex]
so dx=3*sec[tex]\theta[/tex]*tan[tex]\theta[/tex] d[tex]\theta[/tex]
When I substitute that in and simplify it, I got:
27*[tex]\int(sec^4(\theta) d\theta)[/tex]
And I don't know how to integrate that. Half angle formulas aren't seeming to work.
Thanks!