Question Finding antiderivative

tradBohus

New member
Joined
Feb 2, 2021
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8
I am meant to find this antiderivative without a calculator.
1616348606683.png
I know the answer is 1616348645377.png.
I know I would need to use the product rule and chain rule "in reverse", just don't know how to go about it.
Any help? Thanks!
 

Jomo

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Joined
Dec 30, 2014
Messages
10,568
1st of all, the given answer is incomplete.
2ndly, to receive help from this forum we need to know where you need help. It would be best if you show us your work so we can tell you where you went wrong and give you some hints. Please post back.
 

tradBohus

New member
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Feb 2, 2021
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8
Of course, thanks for the feedback. I haven't gotten far:
I have integrated the third degree polynomial to be 1616350113862.png.
I am stuck at integrating e-22+16t.
 

Dr.Peterson

Elite Member
Joined
Nov 12, 2017
Messages
11,538
I am meant to find this antiderivative without a calculator.
View attachment 25915
I know the answer is View attachment 25916.
I know I would need to use the product rule and chain rule "in reverse", just don't know how to go about it.
Any help? Thanks!
The chain rule in reverse is substitution; the product rule in reverse is integration by parts. Both will probably be useful. Have you tried either?

Of course, thanks for the feedback. I haven't gotten far:
I have integrated the third degree polynomial to be View attachment 25918.
I am stuck at integrating e-22+16t.
You can't just integrate each factor and multiply them together; so why do you think you need to do this? To integrate by parts, you generally choose a "part" that you can integrate.
 

Jomo

Elite Member
Joined
Dec 30, 2014
Messages
10,568
Of course, thanks for the feedback. I haven't gotten far:
I have integrated the third degree polynomial to be View attachment 25918.
I am stuck at integrating e-22+16t.
Why would you integrate that 3rd degree polynomial? Do you plan on using using by parts. Remember that \(\displaystyle \int f(x)g(x)\neq\int f(x)dx\int g(x)dx.\)

If it did, then integral would have multiple answers since \(\displaystyle \int f(x)dx = \int 1*f(x)dx = \int1dx \int f(x) dx = x\int f(x)dx = x\int 1*f(x)dx = x\int 1dx \int f(x)dx =x^2\int f(x)dx =...\)
 
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