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Math Help - Intergration

  1. #1
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    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.
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Gigabyte View Post
    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 u=x^4-1
    then du=4x^3

    So then you have

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

    For the second one use parts

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

    then

    dv=e^xdx\Rightarrow{v=e^x}
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  3. #3
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Gigabyte View Post
    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 u=x^4+1 for the first

    and then for the second

    use parts letting

    x+1=u

    and dv=e^xdx
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  4. #4
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Gigabyte View Post
    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 e^x term:

    xe^x+e^x.

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

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

    Hope this makes sense!!
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  5. #5
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Gigabyte View Post
    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:
    y = e^{f(x)}

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

    -Dan
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