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If int(x+(cos^(-1)3x)^(2))/(sqrt(1-9x^(2...

If `int(x+(cos^(-1)3x)^(2))/(sqrt(1-9x^(2)))dx=Asqrt(1-9x^(2))+B(cos^(-1)3x)^(3)+C,` then A-B is

A

`(2)/(9)`

B

`-(1)/(9)`

C

`(1)/(9)`

D

0

Text Solution

Verified by Experts

The correct Answer is:
D
`int(x+(cos^(-1)3x)^(2))/(sqrt(1-9x^(2)))dx=int(x)/(sqrt(1-9x^(2)))dx+int((cos^(-1)3x)^(2))/(sqrt(1-9x^(2)))dx`
`=-(1)/(18)2sqrt(1-9x^(2))-(1)/(9)(cos^(-1)3x)^(3)+C`
`therefore" "A=-(1)/(9),B=-(1)/(9)`
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