Evaluate ∫$$(1+x)3xdx$$

Correct option is 12x+2x3/2+65x5/2+27x7/2+c

Questions

$Evaluate \int \frac{(1 + x)^{3}}{\sqrt{x}} d x$

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2x+2x3/2+65x5/2+27x7/2+c

2x+x3/2+65x5/2+27x7/2+c

2x+2x3/2+25x5/2+27x7/2+c

2x+23x3/2+65x5/2+27x7/2+c

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detailed solution

Correct option is A

∫(1+x)3xdx=∫1+3x+3x2+x3xdx=∫x−1/2dx+3∫x1/2dx+3∫x3/2dx+∫x5/2dx=x1/21/2+3x3/23/2+3⋅x5/25/2+x7/27/2+c=2x+2x3/2+65x5/2+27x7/2+c

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Evaluate ∫(1+x)3xdx

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$Evaluate \int \frac{(1 + x)^{3}}{\sqrt{x}} d x$