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Question
Integrate the following functions w.r.t. x : e3logx(x4 + 1)–1
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Solution
Let I = e3logx(x4 + 1)–1.dx
= `int e^(logx^3)/(x^4 + 1).dx`
= `int x^3/(x^4 + 1).dx` ...[∵ elogN = N]
= `(1)/(4) int(4x^3)/(x^4 + 1).dx`
= `(1)/(4) int(d/dx(x^4 + 1))/(x^4 + 1).dx`
= `(1)/(4)log|x^4 + 1| + c. ...[∵ int (f'(x))/f(x) dx = log|f(x)| + c]`
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