$(a)\;\frac{1}{2} \tan ^{-1} \bigg(\frac{\sqrt {\tan \theta } -1/ \sqrt {\tan \theta }}{\sqrt 2}\bigg) -\frac{1}{2 \sqrt 2 } \log \bigg(\frac{\sqrt {\tan \theta}+\frac {1}{\sqrt {\tan \theta }}-\sqrt 2 }{\sqrt {\tan \theta}+ \frac{1}{\sqrt {\tan \theta}}+\sqrt 2 }\bigg)+c \\(b)\;\frac{5}{2} \tan ^{-1} \bigg(\frac{\sqrt {\tan \theta } -1/ \sqrt {\tan \theta }}{\sqrt 2}\bigg) -\frac{1}{2 \sqrt 2 } \log \bigg(\frac{\sqrt {\tan \theta}+\frac {1}{\sqrt {\tan \theta }}-\sqrt 2 }{\sqrt {\tan \theta}+ \frac{1}{\sqrt {\tan \theta}}+\sqrt 2 }\bigg)+c \\(c)\;\frac{1}{2} \tan ^{-1} \bigg(\frac{\sqrt {\tan \theta } +1/ \sqrt {\tan \theta }}{\sqrt 2}\bigg) -\frac{1}{2 \sqrt 2 } \log \bigg(\frac{\sqrt {\tan \theta}+\frac {1}{\sqrt {\tan \theta }}-\sqrt 2 }{\sqrt {\tan \theta}+ \frac{1}{\sqrt {\tan \theta}}+\sqrt 2 }\bigg)+c \\ (d)\;None$
