Question

find the indefinite integral. ∫1/3x+2 dx

Answer 1

Is this it?
\[\int\limits_{}^{}(\frac{1}{3}x+2)\ dx\]

Answer 2

not 1/3

Answer 3

1 is the only umber in the numerator

Answer 4

@kropot72

Answer 5

So it is
\[\int\limits_{}^{}(\frac{1}{3x}+2)\ dx\]
Correct?

Answer 6

put the +2 next to the 3x and yu got it lol

Answer 7

Got it!
\[\int\limits_{}^{}\frac{1}{3x+2}\ dx\]

Answer 8

lol yes! (:

Answer 9

I think your helper left. This is a simple integral. Most people would use a u-substitution, so I will do so as well.

Let u=3x +2, then
du =3dx.

Solving for dx, we get that \[\frac{ du }{ 3 }=dx\]

Now, substituting all of this into your integral, you get:

\[\frac{ 1 }{ 3 } \int\limits{\frac{ du }{ u}}=\frac{ 1 }{ 3}\ln \left| u \right| +c\]

Now, go back and replace u. We get

\[\frac{ 1 }{ 3 }\ln \left| 3x+2 \right|+c\]