a x^3 + b x^2 + c x^4 , ,dx equals to - Vidyadip

MCQ

$\int {\frac{{a{x^3} + b{x^2} + c}}{{{x^4}}}\,\,dx} $ equals to

A
$a\log x + \frac{b}{{{x^2}}} + \frac{c}{{3{x^3}}} + c$
B
$a\log x + \frac{b}{x} - \frac{c}{{3{x^3}}} + c$
✓
$a\log x - \frac{b}{x} - \frac{c}{{3{x^3}}} + c$
D
None of these

✓

Answer

Correct option: C.

$a\log x - \frac{b}{x} - \frac{c}{{3{x^3}}} + c$

c
(c) $I = \int {\frac{{a{x^3} + b{x^2} + c}}{{{x^4}}}dx = \int {\left[ {\frac{a}{x} + \frac{b}{{{x^2}}} + \frac{c}{{{x^4}}}} \right]\,dx} } $
$ = a\log x - \frac{b}{x} - \frac{c}{{3{x^3}}} + c$.

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