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Question

If x5(1+x3)23dx=A(1+x3)83+B(1+x3)53+C, then

A
A=14,B=15
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B
A=18,B=15
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C
A=18,B=15
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D
None of these
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Solution

The correct option is B A=18,B=15
Let 1+x3=t2
3x2dx=2tdt.x5(1+x3)23dx(t21)(t2)23x2dx(t21)(t2)232t3dt=23(t21)t73dt=23(t133t73)dt=23(316t163310t103)+C=18(1+x3)8315(1+x3)53+C

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