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Question
Integrate the following functions w.r.t. x : `(1)/(4x + 5x^-11)`
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Solution
Let I = `int(1)/(4x + 5x^-11).dx`
= `int x_11/(x^11(4x + 5x^-11)).dx`
= `int x^11/(4x^12 + 5).dx`
= `(1)/(48) int(48x^11)/(4x^12 + 5).dx`
= `(1)/(48) int(d/dx(4x^12 + 5))/(4x^12 + 5).dx`
= `(1)/(48)log|4x^12 + 5| + c ...[∵ int (f'(x))/f(x) dx = log|f(x)| + c]`
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