integral(1+cosx)/(1+sinx) dx

asked by guest
on Nov 24, 2024 at 3:21 am



You asked:

Evaluate the integral: \(\int{\frac{1 + \cos\left( x \right)}{1 + \sin\left( x \right)}}dx\)

MathBot Answer:

Antiderivative

\[\int{\frac{1 + \cos\left( x \right)}{1 + \sin\left( x \right)}}dx = - \frac{2}{1 + \tan{\left(\frac{x}{2} \right)}} - \frac{\log{\left(1 + \tan^{2}{\left(\frac{x}{2} \right)} \right)}}{1 + \tan{\left(\frac{x}{2} \right)}} + \frac{2 \log{\left(1 + \tan{\left(\frac{x}{2} \right)} \right)}}{1 + \tan{\left(\frac{x}{2} \right)}} - \frac{\log{\left(1 + \tan^{2}{\left(\frac{x}{2} \right)} \right)} \tan{\left(\frac{x}{2} \right)}}{1 + \tan{\left(\frac{x}{2} \right)}} + \frac{2 \log{\left(1 + \tan{\left(\frac{x}{2} \right)} \right)} \tan{\left(\frac{x}{2} \right)}}{1 + \tan{\left(\frac{x}{2} \right)}} + C\]

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