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Evaluate (i) int((2x+5))/((x^(2)+5x+9)...

Evaluate
(i) `int((2x+5))/((x^(2)+5x+9))dx` (ii) `int((6x-7))/((3x^(2)-7x+5))dx`
(iii) `int((cosx-sinx))/((cosx+sinx))dx` (iv) `int(sec x)/(log(secx+tanx))dx`

Text Solution

AI Generated Solution

Let's evaluate the given integrals step by step. ### (i) Evaluate \( \int \frac{2x + 5}{x^2 + 5x + 9} \, dx \) **Step 1:** Let \( t = x^2 + 5x + 9 \). Then, differentiate \( t \) with respect to \( x \): \[ dt = (2x + 5) \, dx \] ...
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