Thread: 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.

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
then

So then you have

integrate that and backsub

For the second one use parts

Let

then

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 for the first

and then for the second

use parts letting



and

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 term:

.

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



Hope this makes sense!!

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:




-Dan