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Integrate the functions(sinx)/((1+cosx)^...

Integrate the functions`(sinx)/((1+cosx)^2)`

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To solve the integral \( \int \frac{\sin x}{(1 + \cos x)^2} \, dx \), we can follow these steps: ### Step 1: Substitution Let \( t = 1 + \cos x \). Then, we differentiate both sides: \[ dt = -\sin x \, dx \quad \Rightarrow \quad \sin x \, dx = -dt \] ...
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Knowledge Check

  • The range of the function f(x)=1/abs(sinx)+1/abs(cosx) is

    A
    `[2sqrt(2),infty)`
    B
    `(sqrt(2),2sqrt(2))`
    C
    `(0,2sqrt(2))`
    D
    `(2sqrt(2),4)`

  • The derivative of the function, f(x)=cos^(-1){(1)/(sqrt(13))(2cosx-3sinx)}+sin^(-1){(1)/(sqrt(13))(2cosx+3sinx)}w.r.tsqrt(1+x^(2)) is

    A
    2x
    B
    `2sqrt(1+x^(2))`
    C
    `(2)/(x)sqrt(1+x^(2))`
    D
    `(2x)/(1+x^(2))`

    • Similar Questions

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    The number of integers in the range of the function f(x)=|4((sqrt(cosx)-sqrt(sinx))(sqrt(cosx)+sqrt(sinx)))/((cosx+sinx))| is ________.

    Evaluate the following integrals: int(1+sinx)/(sin x(1+cosx))dx

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