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Evaluate the following : int(0)^(pi//...

Evaluate the following :
`int_(0)^(pi//4)(sec^(2)x)/(tan^(2)x+4 tanx+1)dx`

Text Solution

AI Generated Solution

To evaluate the integral \[ I = \int_{0}^{\frac{\pi}{4}} \frac{\sec^2 x}{\tan^2 x + 4\tan x + 1} \, dx, \] we will use the substitution \( t = \tan x \). ...
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Knowledge Check

  • int_(0)^(pi//4) (sec^(2)x)/((1+tan x)(2+tan x))dx is equal to

    A
    `log_(e)((2)/(3))`
    B
    `log_(e)3`
    C
    `(1)/(3)log_(e)((4)/(3))`
    D
    `log_(e)((4)/(3))`

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