Math

Indefinite Integration Solutions

8. [2.1/7.71 Points]
DETAILS
PREVIOUS ANSWERS
LARCALCET7 5.8.502.XP.MI.SA.
MY NOTES
ASK YOUR TEACHER
This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any
points for the skipped part, and you will not be able to come back to the skipped part.
Tutorial Exercise
Find the integral.
6x + 5
dx
Step 1
Split the integrand
6x + 5
dx into two parts.
Vi - x^
6x + 5
dx =
6x
V1
5
_dx
dx +
V1 - x2
2x
I * 5. dx = <& 3 )
dx +
dx
Step 2
2x
In
6x + 5
dx = 3
- x²
dx, the first term, 3
dx fits the Power
Rule and the second term 5
5/
dx fits the Arcsine
Arcsine Rule.
Step 3
2x
Now, consider the term 3
dx and first, use substitution to make the integrand simpler.
2
Let u = X
Then, du =
2 x dx.
Step 4
Rewrite the integrand in terms of u.
dx = 3
du
dx
V1-u
Apply the Power Rule of integration and simplify.
du
3/ 7
=
(1 - u)
1/
(-1) +
(1 - u
JO+C
Substitute for u in terms of x to write the expression in terms of x.
2x
dx =
(1-
Ota
Submit
Skip_(you cannot come back)