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Question
Evaluate:
`int(2x^3 - 1)/(x^4 + x)dx`
Solution
`int(2x^3 - 1)/(x^4 + x)dx`
Dividing both nominator and denominator by ‘x’ we get
Let `x^2 + 1/x = t`
`\implies (2x - 1/x^2)dx = dt`
= `int(2x - 1/x^2)/(x^2 + 1/x)dx`
= `int dt/t`
= `log_e|t| + c`
= `log_e|x^2 + 1/x| + c`
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