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7.1 inderfinite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.1 inderfinite integral1 Mark
MCQ
$\int_{}^{} {\frac{{a{x^{ - 2}} + b{x^{ - 1}} + c}}{{{x^{ - 3}}}}} \;dx = $
  • A
    $2a{x^2} + 3b{x^3} + 4c{x^4} + k$
  • B
    $6a{x^2} + 4b{x^3} + 3c{x^4} + k$
  • C
    $a + b + c{x^2} + k$
  • ✓
    $\frac{1}{2}a{x^2} + \frac{1}{3}b{x^3} + \frac{1}{4}c{x^4} + k$
✓

Answer

Correct option: D.
$\frac{1}{2}a{x^2} + \frac{1}{3}b{x^3} + \frac{1}{4}c{x^4} + k$
d
(d)$\int_{}^{} {\frac{{a{x^{ - 2}} + b{x^{ - 1}} + c}}{{{x^{ - 3}}}}\,dx} = \int_{}^{} {(ax + b{x^2} + c{x^3})\,dx} $
$ = \frac{1}{4}c{x^4} + \frac{1}{3}b{x^3} + \frac{1}{2}a{x^2} + k.$

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