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Question
`int ("e"^(3x))/("e"^(3x) + 1) "d"x`
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Solution
Let I = `int ("e"^(3x))/("e"^(3x) + 1) "d"x`
Put e3x + 1 = t
Differentiating w.r.t. x, we get
3e3xdx = dt
∴ e3xdx = `"dt"/3`
∴ I = `int 1/"t"* "dt"/3 = 1/3 log |"t"| + "c"`
∴ I `1/3 log|"e"^(3x) + 1| + "c"`
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