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STD 12 - 7.1 inderfinite integral — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 7.1 inderfinite integral1 Mark
MCQ
$\int_{}^{} {{x^3}\sqrt {3 + 5{x^4}} } \;dx = $
  • A
    ${(3 + 5{x^4})^{3/2}} + c$
  • B
    $\frac{1}{5}{(3 + 5{x^4})^{3/2}} + c$
  • ✓
    $\frac{1}{{30}}{(3 + 5{x^4})^{3/2}} + c$
  • D
    None of these
✓

Answer

Correct option: C.
$\frac{1}{{30}}{(3 + 5{x^4})^{3/2}} + c$
c
(c) Put $3 + 5{x^4} = t \Rightarrow 20{x^3}dx = dt,$ then
$\int_{}^{} {{x^3}\sqrt {3 + 5{x^4}} dx} = \frac{1}{{20}}\int_{}^{} {{t^{12}}dt} $
$ = \frac{2}{3} \times \frac{1}{{20}}.{t^{3/2}} + c = \frac{1}{{30}}{(3 + 5{x^4})^{3/2}} + c.$

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