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An antiderivative of the integral inte^(...

An antiderivative of the integral `inte^(x)((1-x)/(1+x))^(2)dx` is

A

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

B

`(-xe^(x))/((1+x^(2))^(2))`

C

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

D

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

Text Solution

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The correct Answer is:
D
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Knowledge Check

  • The value of the integral int_(0)^(1) x (1-x)^(n) dx is

    A
    `(1)/(n+1) + (1)/(n+2)`
    B
    `(1)/((n+1) (n+2))`
    C
    `(1)/(n+2) - (1)/(n+1)`
    D
    `2((1)/(n+1)- (1)/(n+2))`

  • The value of the integral int_(-a)^(a) (xe^(x^(2)))/(1+x^(2))dx is

    A
    `e^(a^(2))`
    B
    0
    C
    `e^(-a^(2))`
    D
    a

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