You need to use the following substitution `2^t + 3 = u` , such that:
`2^t + 3 = u=> 2^t*ln 2 dt= du => 2^t*dt= (du)/(ln 2 )`
`int (2^t*dt)/(2^t + 3 ) = (1/(ln 2))*int (du)/u`
`(1/(ln 2))*int (du)/u = (1/(ln 2))*ln|u| + c`
Replacing back `2^t + 3` for u yields:
`int (2^t*dt)/(2^t + 3 ) = (1/(ln 2))*ln(2^t + 3) + c`
Since `2^t + 3 > 0` yields that `ln|2^t + 3| = ln(2^t + 3)`
Hence, evaluating the indefinite integral, yields `int (2^t*dt)/(2^t + 3 ) = (ln(2^t + 3))/(ln 2) + c.`
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