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3.2 Integration by substitution

1.

(a) $\displaystyle{-e^{2 - x}}$(b) $\displaystyle{-\tan (1 - x)}$(c) $\displaystyle{-{\sqrt{1 - {x^2}}}}$(d) $\displaystyle{\sec(x)}$

(e) $\displaystyle{- e^{\frac{1}{x}}}$(f) $\displaystyle{\frac{2 {\sqrt{1 + 3 \tan (\theta)}}}{3}}$(g) $\displaystyle{-2 x - 2 \cot (x)}$(h) $\displaystyle{\frac{1}{2}(\log (x))^2}$

(i) $\displaystyle{\tan^{-1} ({e^x})}$(j) $\displaystyle{\frac{-\cos ({x^2})}{2}}$