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Question
Integrate the following functions w.r.t. x : `e^(3x)/(e^(3x) + 1)`
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Solution
Let I = `int e^(3x)/(e^(3x) + 1).dx`
Put e3x + 1 = t.
∴ 3e3x dx = dt
∴ e3x dx = `dt/(3)`
∴ I = `int (1)/t.dt/(3)`
= `(1)/(3) int (1)/t dt`
= `(1)/(3)log|t| + c`
= `(1)/(3)log|e^(3x) + 1| + c`.
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