∫14x+5x-11 dx - Mathematics and Statistics

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Sum

`int 1/(4x + 5x^(-11))  "d"x`

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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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Chapter 2.3: Indefinite Integration - Short Answers I

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