Question #70eda
3 Answers
Explanation:
We know that :
we use integration by parts, https://en.wikipedia.org/wiki/Integration_by_parts
Integrals of the form
Explanation:
I assume that you are using
Integrate by parts with
Integrate by parts with
# = 2/3x^(3/2)logx - 2/3 int x^(3/2) x^-1 dx#
# = 2/3x^(3/2)logx - 2/3 int x^(1/2) dx#
# = 2/3x^(3/2)logx - 2/3 (2/3x^(3/2))#
# = 2/3x^(3/2)logx - 4/9 x^(3/2)#
Finish by evaluating from
General case
The integral
Bonus Example 1
Integrate by parts with
# = 1/4x^4logx-1/4 int x^3 dx# (We integrated#x^3# in step 1.)
Bonus Example 2
Integrate by parts with
# = -1/6x^-6logx+ 1/6 int x^-7 dx# (We integrated#x^-7# in step 1.)
Two more bonuses
One:
We use the same method to find
Two:
If you like, you can work out the general rule for
Explanation:
Let,
We use the following Rule of Integration by Parts (IBP) :
IBP :
We take :