# Question Finding antiderivative

##### New member
I am meant to find this antiderivative without a calculator.

I know the answer is .
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

##### Elite Member
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.

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

#### Dr.Peterson

##### Elite Member
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
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 $$\displaystyle \int f(x)dx = \int 1*f(x)dx = \int1dx \int f(x) dx = x\int f(x)dx = x\int 1*f(x)dx = x\int 1dx \int f(x)dx =x^2\int f(x)dx =...$$