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(x)/(1+sinx)...

`(x)/(1+sinx)`

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`int (x)/(1+sinx)dx=int (x(1-sinx))/((1+sinx)(1-sinx))dx`
`=int (x(1-sinx))/((1-sin^(2)x))dx`
`=int f x((1-sinx)/(cos ^(2)x))dx `
`=int x((1)/(cos^(2)x)-(sin x)/(cos x)xx(1)/(cos x))dx`
`=int fx(sec^(2)x-sec xtan x)dx`
`=int x sec^(2)xdx-int sec x tan x dx`
`=x int sec^(2)xdx-int [(d)/(dx)(x)int sec^(2)xdx]dx`
`-{x int sec x tan x dx-int [(d)/(dx)(x)int sec x.tan x dx]dx}`
`=x tan x-int 1.tan x dx-x sec x +int 1.sec x dx`
`=x tan x-log |sec x|-x sec x+log|sec x+tan x|+c`
`=x tan x-log |sec x|-x sec x+log |sec x+tan x|+c`
`=x (tan x-sec x)-log sec(x)+log|sec x+tan x|+c`
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