Given: =∫1x^5( 1 + x^4)dx =∫(1x^5+1x)dx =∫1x^5dx+∫1xdx = 14x^4+ln x +constant ...

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Integration by Substitution

Solve ∫1x5 ...

Question

Solve $\int \frac{1}{x^{5}} (1 + x^{4}) d x$

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Solution

Given:
$= \int \frac{1}{x^{5}} (1 + x^{4}) d x$
$= \int (\frac{1}{x^{5}} + \frac{1}{x}) d x$
$= \int \frac{1}{x^{5}} d x + \int \frac{1}{x} d x$
$= \frac{- 1}{4 x^{4}} + ln x + c o n s t a n t$

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