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int (0)^(1) (x)/(x^(2)+1)dx...

`int _(0)^(1) (x)/(x^(2)+1)dx`

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To solve the integral \( I = \int_{0}^{1} \frac{x}{x^2 + 1} \, dx \), we can use a substitution method. Here’s a step-by-step solution: ### Step 1: Choose a substitution Let \( u = x^2 + 1 \). Then, we need to find \( du \): \[ du = 2x \, dx \quad \Rightarrow \quad \frac{du}{2} = x \, dx \] ...
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Knowledge Check

  • If int_(0)^(1) (e^(x))/( 1+x) dx = k , then int_(0)^(1) (e^(x))/( (1+x)^(2)) dx is equal to

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

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    If I_(1)=int_(0)^(oo) (dx)/(1+x^(4))dx and I_(2)=underset(0)overset(oo)int x^(2)(dx)/(1+x^(4))"then"n (I_(1))/(I_(2))=

    int_(0)^(1)x^2dx

    Evaluate: int_(0)^(1)(xe^(x))/(1+x)^(2) dx

    Let I= int_(0)^(1) (e^(x))/( x+1) dx, then the vlaue of the intergral int_(0)^(1) (xe^(x^(2)))/( x^(2)+1) dx, is

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