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int(cosx+xsinx)/(x^(2)+xcosx)dx= . . . ...

`int(cosx+xsinx)/(x^(2)+xcosx)dx= ` . . . .

A

`log|(xsinx)/(x+cosx)|+c`

B

`log|(x)/(x+cosx)|+c`

C

`log|(xsinx)/(x+cosx)|+c`

D

`log|x^(2)+xcosx|+c`

Text Solution

Verified by Experts

The correct Answer is:
B
`int(cosx+xsinx)/(x^(2)+xcosx)dx=int(cosx+xsinx+x-x)/(x(x+cosx))dx`
`=int((cosx+x)+x(sinx-1))/(x(x+cosx))dx`
`=int(1)/(x)dx+int(sinx-1)/(x+cosx)dx`
`=log|x|-int(1-sinx)/(x+cosx)dx`
`=log|x|-log(x+cosx)+c`
`=log|(x)/(x+cosx)|+c`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-SOLVED PAPER 2019-MCQS
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  14. In DeltaABC, with usual notations, if cosA=(sinB)/(sinC), then the tri...

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  15. In a GP if the (m+n)th term is p and (m-n)th term is q then mth term i...

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  16. A random variable X has following probability distribution {:(X=x,1,...

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