Question

help me with this integration :

1/2 \[\int\limits_{?}^{?} (4x + 6)/\sqrt{2x^2 +6x -1}\] dx

Answer 1

What's the question mark>

Answer 2

there no limit..leave the answer in terms of x

Answer 3

Let u = 2x^2 + 6x - 1
du/ 4x + 6

Answer 4

\[2\sqrt{2x^2+6x-1}\]

Answer 5

\[\int\limits\frac{4x+6}{\sqrt{2x^{2}+6x-1}} \]
Let u = 2x^2 +6x - 1
\[\int\limits\frac{4x+6}{\sqrt{u}} *\frac{du}{4x+6} \]
\[\int\limits\frac{1}{\sqrt{u}}du = \int\limits\frac{u^{1//2}}{1/2} \]
\[\frac{(2x^{2}+6x-1)^{1/2}}{1/2} + C\]

Answer 6

Note that the original question has a factor (1/2) written above the integral.
If that's the case, both results have to be divided by 2.

Answer 7

I dont think that the (1/2) is related to the integral :/

Answer 8

Perhaps, but it can also happen when the 1/2 was typed in before entering the "equation" button, which makes the integral go to a separate line.
In any case, the results correspond clearly to the integral without the (1/2).

Answer 9

Ohh woops, my bad i misunderstood the question, sorry.
I thought the (1/2) was nothing xD