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int(logtanx)/(sinxcosx)dx=?...

`int(logtanx)/(sinxcosx)dx=?`

A

`log{log(tanx)}+C`

B

`(1)/(2)(logtanx)^(2)+C`

C

`log(sinxcosx)+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Put log tan x=t. Then, `(1)/(tanx)*sec^(2)xdx=dt,i.e.,(1)/(sinxcosx)dx=dt`.
`:." "Iinttdt=(1)/(2)t^(2)+C=(1)/(2)(log tanx)^(2)+C`.
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Knowledge Check

  • int(sqrt(tanx))/(sinxcosx)dx is equal to.

    A
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    B
    `2sqrt(cotx)+C`
    C
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    D
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  • If int(sqrt(cotx))/(sinxcosx)dx=Psqrt(cotx)+Q, then the value of P is

    A
    `-2`
    B
    2
    C
    3
    D
    `-3`

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