If x^3dx 1+x^2 =a(1+x^2)^ 3 2 +b 1+x^2 +c, then: - Vidyadip

MCQ

If $\int\frac{\text{x}^3\text{dx}}{\sqrt{1+\text{x}^2}}=\text{a}(1+\text{x}^2)^{\frac{3}{2}}+\text{b}\sqrt{1+\text{x}^2}+\text{c,}$ then:

A
$\text{a}=\frac{1}{3},\text{b}=1$
B
$\text{a}=\frac{-1}{3},\text{b}=1$
C
$\text{a}=\frac{-1}{3},\text{b}=-1$
✓
$\text{a}=\frac{1}{3},\text{b}=-1$

✓

Answer

Correct option: D.

$\text{a}=\frac{1}{3},\text{b}=-1$

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