1. ## Intergration

Hey people, please help. I'm struggling with integrating e^(x+n) type problems. I know that e^x integrates to e^x but i'm just not sure what to do with any other terms.

How would you integrate (8x^3)e^(x^4-1)??? Please could you show all the steps required.

Or just another example (x+1)e^x.

2. Originally Posted by Gigabyte
Hey people, please help. I'm struggling with integrating e^(x+n) type problems. I know that e^x integrates to e^x but i'm just not sure what to do with any other terms.

How would you integrate (8x^3)e^(x^4-1)??? Please could you show all the steps required.

Or just another example (x+1)e^x.
For the first one

Let $\displaystyle u=x^4-1$
then $\displaystyle du=4x^3$

So then you have

$\displaystyle 2\int{e^{u}}du$ integrate that and backsub

For the second one use parts

Let $\displaystyle u=x+1\Rightarrow{du=dx}$

then

$\displaystyle dv=e^xdx\Rightarrow{v=e^x}$

3. Originally Posted by Gigabyte
Hey people, please help. I'm struggling with integrating e^(x+n) type problems. I know that e^x integrates to e^x but i'm just not sure what to do with any other terms.

How would you integrate (8x^3)e^(x^4-1)??? Please could you show all the steps required.

Or just another example (x+1)e^x.
Let $\displaystyle u=x^4+1$ for the first

and then for the second

use parts letting

$\displaystyle x+1=u$

and $\displaystyle dv=e^xdx$

4. Originally Posted by Gigabyte
Hey people, please help. I'm struggling with integrating e^(x+n) type problems. I know that e^x integrates to e^x but i'm just not sure what to do with any other terms.

How would you integrate (8x^3)e^(x^4-1)??? Please could you show all the steps required.

Or just another example (x+1)e^x.
The second one, distribute the $\displaystyle e^x$ term:

$\displaystyle xe^x+e^x$.

To integrate, you need to apply integration by parts to the first one and then directly integrate the second.

$\displaystyle \int xe^x\,dx+\int e^x\,dx=xe^x+C$

Hope this makes sense!!

5. Originally Posted by Gigabyte
Hey people, please help. I'm struggling with integrating e^(x+n) type problems. I know that e^x integrates to e^x but i'm just not sure what to do with any other terms.

How would you integrate (8x^3)e^(x^4-1)??? Please could you show all the steps required.

Or just another example (x+1)e^x.
Use a combination of the chain and product rules:
$\displaystyle y = e^{f(x)}$

$\displaystyle y = e^{f(x)} \cdot f'(x)$

-Dan