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int(e^(6logx)-e^(5logx))/(e^(4logx)-e^(3...

`int(e^(6logx)-e^(5logx))/(e^(4logx)-e^(3logx))dx`

A

`(x)/(2)+C`

B

`(x^(2))/(2)+C`

C

`(x^(3))/(3)+C`

D

`(x^(4))/(2)+C`

Text Solution

Verified by Experts

The correct Answer is:
C
`int(e^(logx)-e^(5logx))/(e^(4logx)-e^(3logx))dx=int(e^(logx^(6))-e^(logx^(5)))/(e^(logx^(4))-e^(logx^(3)))dx`
`=int(x^(6)-x^(5))/(x^(4)-x^(3))dx`
`=int(x^(5)(x-1))/(x^(3)(x-1))dx`
`=intx^(2)dx=(x^(3))/(3)+C`
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