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intx^(3)log x dx is equal to...

`intx^(3)log x dx `is equal to

A

`(x^(4)logx)/4+C`

B

`1/16 [4x^(4)logx-x^(4)]+C`

C

`1/8[x^(4)logxc-4x^(2)]+C`

D

`1/16[4x^(4)logx+x^(4)]+C`

Text Solution

Verified by Experts

The correct Answer is:
B
Let `l=intx^(3)log x dx`
`=(x^(4))/4 logx - int(x^(4))/4 . 1/x dx`
`=(x^(4))/4 logx-int(x^(3))/4dx`
`=(x^(4))/4 log x=(x^(4))/16+C`
`=1/16[4x^(4)logxc-x^(4)]+C`
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