Trigonometric Substitution

[JessicaMX]

Hello. I'm stuck with this integral. Can you help me? Thank you!

 

[tkhunny]

I'm inclined to do the easy part, first.

The part under the radical \(\displaystyle \dfrac{d}{dx}(2-6x-x^{2}) = - 6 - 2x\)

If we can make the numerator look like that, at least part of it will be easy.

 

[HallsofIvy]

Hello. I'm stuck with this integral. Can you help me? Thank you!

If \(\displaystyle u= \frac{x+ 3}{\sqrt{11}}\) then \(\displaystyle x= \sqrt{11}u- 3\).

 

[Deleted member 4993]

Hello. I'm stuck with this integral. Can you help me? Thank you!

You have your topic as trigonometric substitution - why are you making it so complicated?

After your 3 rd. step - substitute:

(x + 3)² = 11 * sin²(Θ)

dx = (√11) * cos(Θ) dΘ

and continue....