How do you find #\int ( \frac { 1} { 3x + 1} ) d x#?
3 Answers
HI,
Lets call
L=
We will add and subtract 3x in numerator .
now,
As L is integrtion of two integrals
Lets take ,
X=
Y=
X can be easily solved
X=
X=x+C (C is constant)
Lets solve Y
Now lets take
3x=t
So, diffrentiate
Substitute "dx" in terms of "dt" in Y
Y=
Y=
Y=
Y=
For this integration you must know formula
As diffrentialtion of (t+1) is 1 this
Y=
Y=
3x=t
hence
Y=
AS we know
L=X-Y
L=
C+C is Another constant C
L=
The answer is
Explanation:
We need
Here,
We perform the substitution
Therefore,
Explanation:
In general
here we have
we note that the top isn't quite the bottom differentiated so let us make an adjustment
so the numerator is now the denominator differentiated
so we integrate using the above relationship