int(dx)/((x+1)sqrt(4x+3)) is equal to...

`int(dx)/((x+1)sqrt(4x+3))` is equal to

A

`tan^(-1)sqrt(4x+3)+C`

B

`3tan^(-1)sqrt(4x+3)+C`

C

`2tan^(-1)sqrt(4x+3)+C`

D

`4tan^(-1)sqrt(4x+3)+C`

Text Solution

Verified by Experts

The correct Answer is:

C

Let `l=int(dx)/((x+1)sqrt(4x+3))`
Put `4x+3=t^(2) rArr 4 dx = 2t dt`
`therefore" "l=(1)/(2)int(tdt)/(((t^(2)-3)/(4)+1)t)=2int(dt)/(1+t^(2))`
`=2tan^(-1)t+C=2tan^(-1)sqrt(4x+3)+C`

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The value of int(dx)/(sqrt(4x-3-x^(2))) is equal to

A

`sin^(-1) (x - 1) + C`

B

`log|(x-2)+sqrt(4x-3-x^(2))|`

C

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int_(8)^(15)(dx)/((x-3)sqrt(x+1)) is equal to

A

`(1)/(2)"log"(5)/(3)`

B

`(1)/(3)"log"(5)/(3)`

C

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D

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int_8^(15)dx/((x-3)sqrt(x+1)) is equal to :

A

`1/2 log 5/3`

B

`1/3 log 5/3`

C

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D

`1/2 log 3/5`

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