how can you get the integral of dy/(x^2 + 9)^2 using trigonometric substitution?

Question

anonymous · Answer

x^2+a^2 --------> x=a tan t

anonymous · Answer

u have a tutorial for this water

anonymous · Answer

Actually @mukushla can get this integral by using trigonometric substitution.

And he did that...

anonymous · Answer

Yes I have but I don't think that I have solved it using trigonometric identity there...

anonymous · Answer

Let me check..

anonymous · Answer

how are you able to integrate this equation if the variable of integration is y ? but the variable in equation is x?

anonymous · Answer

anonymous · Answer

but it is dx?
how about dy?

anonymous · Answer

For dy I think there is no need to evaluate this integral..

anonymous · Answer

The whole term is just a constant if dy is there..

anonymous · Answer

actually the given is this int. dy/(x^2 +9^2).. i just have difficulty because it is dy..

anonymous · Answer

You can take $\frac{1}{x^2 + 9}$ out of the integral..

anonymous · Answer

Check your question if there is dy then in place of x^2 there will y^2 in the denominator..

anonymous · Answer

yes actually that's what i am also thinking about .. but the given is dy and the denominator is x^2 ..

anonymous · Answer

Your question simply evauates to :

$$\frac{1}{(x^2 + 9)^2} \int\limits dy \rightarrow \frac{y}{(x^2 + 9)^2} + C$$

anonymous · Answer

so ur saying that i will assume that 1/ (x^2 + 9)^2 as a constant?

anonymous · Answer

by the way thank you :)

anonymous · Answer

you gave me a BIG help :)

lgbasallote · Answer

it's weird though why it asked for trig sub