Evaluate: (i) `int(tanxsec^2x)/((a+btan^2x)^2)\ dx` (ii) `intsec^3xtanx\ dx`

Explanation

evaluate i)
`I=\int \frac{\tan x \sec ^{2} x}{(a+b \tan ^{2} x)^{2}} d x`
Let
`a+b \tan ^{2} x=t`

`2 b \tan x \sec ^{2} x d x=d t`

`\tan x \sec ^{2} x d x=\frac{d t}{2 b}`
substituting in (1) we have

` I =\int \frac{d t}{2 b t} `


`I=\frac{1}{2 b}) \frac{d t}{t} `


`I=2 b(\log t+c) `

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