How Can I Solve This Integral Using Trigonometric Substitution?

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The integral discussed is ∫1/√((4+9x²)³)dx, and the original poster is seeking a method to solve it using trigonometric substitution. They express frustration at not being able to find a solution despite knowing the answer from other sources. A suggestion is made to use the substitution 3x=2tan(t), which the poster finds helpful. The discussion emphasizes the importance of trying trigonometric substitution for integrals involving square roots. The poster ultimately appreciates the guidance received from the forum.
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Homework Statement


\int1/\sqrt{(4+9x^2)^3}dx




3. The Attempt at a Solution :

i think i do all options that i now, but i cannt to make a solution of this, (the way)? may be anybody can help me,
 
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You can get the answer here: http://integrals.wolfram.com/index.jsp

Enter 1/(Sqrt((4+9*x*x)^3))

Maybe once you have the answer it will give you some ideas about how to solve it.

If you still need help, come back and let us know.
 
eeeeeeeeemmmh thnks, the answer i know, and in others sites,i gave the same answer,

but i want to see the way... :(((((((((((
 
Welcome to PF!

Hi sania16! Welcome to PF! :smile:

(have a square-root: √ and an integral: ∫ and try using the X2 tag just above the Reply box :wink:)

sania16 said:
eeeeeeeeemmmh thnks, the answer i know, and in others sites,i gave the same answer,

but i want to see the way... :(((((((((((

Quite right! :smile:

Hint: for √(a ± bx2), always try a trig substitution first. :wink:​
 
yes you right ! thank you.

i change 3x=2tg(t), and everything being cool!

thanks to all of you!

p.s: how much time i spend on this... :(
 

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