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intx^(2)e^(x)dx=...

`intx^(2)e^(x)dx=`

A

`e^(x)(x^(2)-1)+c`

B

`e^(x)(x^(2)+2x+1)+c`

C

`e^(x)(x^(2)-2x+2)+c`

D

none

Text Solution

Verified by Experts

The correct Answer is:
C
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Knowledge Check

  • intx^(23)e^(5x)dx=

    A
    `e^(5x)[(x^(3))/(5)-(3x^(2))/(25)+(6x)/(125)-(6)/(625)]+c`
    B
    `e^(5x)[(x^(3))/(5)-(3x^(2))/(25)-(6x)/(125)-(6)/(625)]+c`
    C
    `e^(5x)[(x^(3))/(5)+(3x^(2))/(25)+(6x)/(125)-(6)/(625)]+c`
    D
    `e^(5x)[(x^(3))/(5)-(3x^(2))/(25)+(6x)/(125)+(6)/(625)]+c`

  • int(x+1)^(2)e^(x)dx=

    A
    `x^(2)+c`
    B
    `x^(2)e^(x)+c`
    C
    `(x+1)x^(x)+c`
    D
    `(x^(2)+1)e^(x)+c`

  • If I_(n)= intx^(n) e^(cx) dx for n ge 1 , then c, I_(n) + nI_(n-1) is equal to

    A
    `x^(n)e^(cx)`
    B
    `x^(n)`
    C
    `e^(cx)`
    D
    `x^(n) + e^(cx)`

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    int x^4 e^(2x)dx=

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    int (3-x^(2))/(1-2x+x^(2))e^(x)dx=e^(x)f(x)+c rArr f(x)=

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