The following integral ∫ π 4 π 2 2   c o s e c   x 17   d x is equal to

1. $\underset{0}{\overset{\log \left(1+\sqrt{2}\right)}{\int }}2{\left({\mathrm{e}}^{\mathrm{u}}+{\mathrm{e}}^{-\mathrm{u}}\right)}^{16}\mathrm{ }\mathrm{d}\mathrm{u}$
2. $\underset{0}{\overset{\log (1+\mathrm{ }\sqrt{2})}{\int }}{\left({\mathrm{e}}^{\mathrm{u}}+{\mathrm{e}}^{-\mathrm{u}}\right)}^{17}\mathrm{ }\mathrm{d}\mathrm{u}$
3. $\underset{0}{\overset{\log (1+\sqrt{2})}{\int }}{\left({\mathrm{e}}^{\mathrm{u}}-{\mathrm{e}}^{-\mathrm{u}}\right)}^{17}\mathrm{ }\mathrm{d}\mathrm{u}$
4. $\underset{0}{\overset{\log (1+\sqrt{2})}{\int }}2\mathrm{ }{\left({\mathrm{e}}^{\mathrm{u}}-{\mathrm{e}}^{-\mathrm{u}}\right)}^{16}\mathrm{ }\mathrm{d}\mathrm{u}$

Solution

Asked in: JEE Advanced 2014 (Paper 2)

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