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Question

If dxx3(1+x6)2/3=xf(x)(1+x6)1/3+C where C is a constant of integration, then the function f(x) is equal to :

A
16x3
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B
12x2
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C
12x3
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D
3x2
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Solution

The correct option is C 12x3
I=dxx3(1+x6)2/3

=dxx7(1+1x6)2/3

Let 1+1x6=t6x7dx=dt
I=16dtt2/3
=36t1/3+C
=12(1+1x6)1/3+C
=12x2(1+x6)1/3+C

f(x)=12x3

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