Pembuktian Integral cot x dx = ln |sin x| + C


\int cot x dx = \int \frac{cos \quad x}{sin \quad x} dx

= \int \frac{cos \quad x}{sin \quad x} \quad \frac{d(sin \quad x)}{cos \quad x}

= \int \frac{1}{sin \quad x} d(sin x)

misal : sin x = u kemudian substitusi

= \int \frac{1}{u} du

= ln |u| + C

substitusi lagi u = sin x, sehingga

= ln |sin x| + C \blacksquare

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