Evaluate: (i) `int1/(x^2)cos^2(1/x)\ dx` (ii) `intsec^4xtanx\ dx`

Explanation

(i)

`int frac{1}{x^{2}} cdot cos ^{2}(frac{1}{x}) d x `

`text { Let } frac{1}{x}=t `

`Rightarrow-frac{1}{x^{2}}=frac{d t}{d x} `

`Rightarrow frac{1}{x^{2}} d x=-d t `

Now, `int frac{1}{x^{2}} cdot cos ^{2}(frac{1}{x}) d x `

`=-int cos ^{2} t d t `

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