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Question
`int 1/(4x + 5x^(-11)) "d"x`
Solution
Let I = `int 1/(4x + 5x^(-11)) "d"x`
= `int 1/(4x + 5/x^11) "d"x`
= `int x^11/(4x^12 + 5) "d"x`
Put 4x12 + 5 = t
Differentiating w.r.t. x, we get
4(12)x11dx = dt
∴ x11dx = `1/48 "dt"`
∴ I = `1/48 int "dt"/"t"`
= `1/48 log |"t"| + "c"`
∴ I = `1/48 log |4x^12 + 5| + "c"`
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