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Integrate with respect to x: i) (2x+3)...

Integrate with respect to x:
i) `(2x+3)^(5)`, ii) `sin2x`, iii) `sec^(2)(4x+5)`, iv) `sec(3x+2)`, v) `tan(2x+1) `, vi) `2^(3x+4)`
vii) `1/(2x+1)` viii) `e^(4x+5)`

Text Solution

AI Generated Solution

Let's solve the given integration problems step by step. ### i) Integrate `(2x + 3)^(5)` To integrate `(2x + 3)^(5)`, we can use the formula for integration of the form `(ax + b)^(n)`: \[ \int (ax + b)^{n} \, dx = \frac{(ax + b)^{n+1}}{a(n+1)} + C ...
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