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Q.

Evaluate ∫(1+x)3xdx

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a

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

b

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

c

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

d

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

answer is A.

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Detailed Solution

∫(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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