How to integrate $\int_0^{\pi /2} {\frac{{dx}}{{{{\left( {{a^2}{{\cos }^2}x + {b^2}{{\sin }^2}x} \right)}^2}}}} $ ~~~~~[NCERT Exemp. Q. 44,Page 166 ]
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$\int {{e^{{{\tan }^{ – 1}}x}}} \left( {\frac{{1 + x + {x^2}}}{{1 + {x^2}}}} \right)dx$ ~~~~~[NCERT Exemp. Q. 39,Page 166 ]
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$\int_0^\pi {\frac{x}{{1 + \sin x}}} $ ~~~~~[NCERT Exemp. Q. 37,Page 165 ]
and $I = \int_0^\pi {\frac{{\pi – x}}{{1 + \sin (\pi – x)}}} dx = \int_0^\pi {\frac{{\pi – x}}{{1 + \sin…