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प्रश्न
Anti-derivative of `(tanx - 1)/(tanx + 1)` with respect to x is ______.
पर्याय
`sec^2 (π/4 - x) + c`
`-sec^2 (π/4 - x) + c`
`log |sec(π/4 - x)| + c`
`- log |sec(π/4 - x)| + c`
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उत्तर
Anti-derivative of `(tanx - 1)/(tanx + 1)` with respect to x is `underlinebb(- log |sec(π/4 - x)| + c)`.
Explanation:
Let I = `int (tanx - 1)/(tanx + 1) dx`
= `- int (1 - tanx)/(1 + tanx)dx`
= `-int (tan π/4 - tanx)/(1 + tan π/4 tanx)dx`
= `-int tan(π/4 - x)dx`
= `-log |sec(π/4 - x)| + c`
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