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Question Number 129946 by bemath last updated on 21/Jan/21

$$\int \frac{\tan \phi +3}{\sin \phi }\mathrm{d}\phi ?$$

Answered by liberty last updated on 21/Jan/21

$$\mathrm{T}=\int (\frac{1}{\cos \phi }+\frac{3}{\sin \phi })\mathrm{d}\phi$$$$\mathrm{T}=\int (\sec \phi +3\csc \phi )\mathrm{d}\phi$$$$\mathrm{T}=\ln \mid \sec \phi +\tan \phi \mid -3\ln \mid \cot \phi +\csc \phi \mid +\mathrm{c}$$$$\mathrm{T}=\ln \mid \frac{1+\sin \phi }{\cos \phi }\mid -3\ln \mid \frac{\cos \phi +1}{\sin \phi }\mid +\mathrm{c}$$$$$$

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