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Question

dx((x1)3(x+2)5]1/4 is equal to

A

34(x1x+4)1/4+C
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B

43(x1x+4)1/4+C
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C

35(x1x+4)1/4+C
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D

53(x1x+4)1/4+C
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Solution

The correct option is B
43(x1x+4)1/4+C
This integral can also be written as
I=dx((x1)3(x+2)5]1/4I=dx(x1x+2)3/4(x+2)2
Now let,
(x1x+2)=tdt=3dx(x+2)2
Thus our integral becomes,
I=131t3/4dt =13(t1/41/4)+C =43t1/4+C =43(x1x+2)1/4+C
Thus, Option b. is correct.

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