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Solving integrals/ 1/1+a*cos(x)

Integral of 1/1+a*cos(x) dx

Limits of integration:

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The solution

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∫0π(acos⁡(x)+1) dx\int\limits_{0}^{\pi} \left(a \cos{\left(x \right)} + 1\right)\, dx 
Integral(1 + a*cos(x), (x, 0, pi))
Detail solution

  1. Integrate term-by-term:

    1. The integral of a constant times a function is the constant times the integral of the function:

      ∫acos⁡(x) dx=a∫cos⁡(x) dx\int a \cos{\left(x \right)}\, dx = a \int \cos{\left(x \right)}\, dx

      1. The integral of cosine is sine:

        ∫cos⁡(x) dx=sin⁡(x)\int \cos{\left(x \right)}\, dx = \sin{\left(x \right)}

      So, the result is: asin⁡(x)a \sin{\left(x \right)}

    1. The integral of a constant is the constant times the variable of integration:

      ∫1 dx=x\int 1\, dx = x

    The result is: asin⁡(x)+xa \sin{\left(x \right)} + x

  2. Add the constant of integration:

    asin⁡(x)+x+constanta \sin{\left(x \right)} + x+ \mathrm{constant}

The answer is:

asin⁡(x)+x+constanta \sin{\left(x \right)} + x+ \mathrm{constant}

The answer (Indefinite) [src] 
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 | (1 + a*cos(x)) dx = C + x + a*sin(x)
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∫(acos⁡(x)+1) dx=C+asin⁡(x)+x\int \left(a \cos{\left(x \right)} + 1\right)\, dx = C + a \sin{\left(x \right)} + x
Simplify
The answer [src] 
pi
π\pi 
=
= 
pi
π\pi 
pi

    Use the examples entering the upper and lower limits of integration.

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