17) ∫ 1 + t a n 2 x d x {\displaystyle \int _{}^{}1+tan^{2}xdx} = ∫ 1 + s i n 2 x c o s 2 x d x {\displaystyle \int _{}^{}1+{\frac {sin^{2}x}{cos^{2}x}}dx} = ∫ c o s 2 x + s i n 2 x c o s 2 x d x {\displaystyle \int _{}^{}{\frac {cos^{2}x+sin^{2}x}{cos^{2}x}}dx} = cos 2 x + s i n 2 x = 1 {\displaystyle \cos ^{2}x+sin^{2}x=1} thus, ∫ 1 c o s 2 x d x {\displaystyle \int _{}^{}{\frac {1}{cos^{2}x}}dx} = <math>\int_{}^{}sec^2xdx
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