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Question
Choose the correct options from the given alternatives :
`int (1)/(x + x^5)*dx` = f(x) + c, then `int x^4/(x + x^5)*dx` =
Options
log x – f(x) + c
f(x) + log x + c
f(x) – log x + c
`(1)/(5) x^5f(x) + c`
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Solution
log x – f(x) + c
[Hint: `int x^4/(x + x^5)*dx = int((x^4 + 1) - 1)/(x(x^4 + 1))*dx`
= `int (1/x - 1/(x + x^5))*dx`
= log x – f(x) + c].
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