Question

integration of 3/√3x+2 dx​

Answer 1

Answer:

begin mathsize 16px style integral straight x square root of 3 straight x minus 2 end root dx

Put space 3 straight x minus 2 equals straight t rightwards double arrow straight x equals fraction numerator straight t plus 2 over denominator 3 end fraction

3 dx equals dt

dx equals dt over 3

integral fraction numerator straight t plus 2 over denominator 3 end fraction cross times square root of straight t dt over 3

Integrate space it space further

end stylebegin mathsize 16px style integral straight x square root of 3 straight x minus 2 end root dx

Put space 3 straight x minus 2 equals straight t rightwards double arrow straight x equals fraction numerator straight t plus 2 over denominator 3 end fraction

3 dx equals dt

dx equals dt over 3

integral fraction numerator straight t plus 2 over denominator 3 end fraction cross times square root of straight t dt over 3

Integrate space it space further

end style

Step-by-step explanation:

Answer 2

Take 3x+2= t^2
On differentiation 3dx= 2tdt
So, dx= 2tdt/3
Replace 3x+2 with t^2 and dx with 2tdt/3.
Then you will get the answer.

I haven’t written the solution completely because my intention is to make you try on your own.

Please mark my answer brainliest if you got what you want.