Calculate : (x^3-1 x + 3x )dx: - Vidyadip

MCQ

Calculate : $\int(\text{x}^3-\frac{1}{\text{x}}+{3\text{x}})\text{dx:}$

A
$\frac{\text{x}^{4}}{3}-\log\text{x}+\frac{\text{5x}^{2}}{2}+\text{c}$
B
$\frac{\text{x}^{4}}{4}-\log\text{x}+\frac{\text{2x}^{2}}{3}+\text{c}$
C
$\frac{\text{x}^{4}}{4}-\log\text{x}+\frac{\text{3x}^{2}}{4}+\text{c}$
✓
$\frac{\text{x}^{4}}{4}-\log\text{x}+\frac{\text{3x}^{2}}{2}+\text{c}$

✓

Answer

Correct option: D.

$\frac{\text{x}^{4}}{4}-\log\text{x}+\frac{\text{3x}^{2}}{2}+\text{c}$

$\int(\text{x}^3-\frac{1}{\text{x}}+{3\text{x}})\text{dx}=\frac{x^4}{4}-\text{ln}\mid{\text{x}}\mid{+}\frac{3\text{x}^2}{2}+\text{c}$

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