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integration

naysa , 11 Years ago
Grade
anser 1 Answers
jagdish singh singh
\hspace{-0.7 cm}$Let $I = \int\frac{\csc^2 x-2005}{\cos^{2005}x}dx = \int \frac{\csc^{2}x}{\cos^{2005}x}dx-\int\frac{2005}{\cos^{2005}}dx$\\\\ Using Integration by parts for $(1)$\\\\ $I = -\frac{\cot x}{\cos^{2005}x}+\int 2005 \cos^{-2006}x\cdot \sin x\cdot \cot xdx-\int\frac{2005}{\cos^{2005}x}dx$\\\\ $I = -\frac{\cot x}{\cos^{2005}x}+\int \frac{2005}{\cos^{2005}x}dx-\int\frac{2005}{\cos^{2005}x}dx$\\\\ $I = \int\frac{\csc^2 x-2005}{\cos^{2005}x}dx = -\frac{\cot x}{\cos^{2005}x}+\mathcal{C}$
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