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Solve the following.
Evaluate: ∫ (1 + cos x)/(sin² x) dx
Evaluate: $\int \frac{1 + \cos x}{\sin^2 x}\,dx$
Answer
Answer
Integral: $\int \left((1+cos(x))/sin(x)^2\right) dx$
$\int \frac{1+\cos x}{\sin^2 x}dx = \int \operatorname{cosec}^2 x\,dx + \int \operatorname{cosec} x\cot x\,dx$
$= -\cot x - \operatorname{cosec} x + C$
Hence the result is $-\cot x - \operatorname{cosec} x + C$.
Final answer: $-\cot x - \operatorname{cosec} x + C$