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Evaluate the definite integrals `int_(0)^(pi//4)(sinx+cosx)/(25-16(sinx-cosx)^(2)) dx`

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The correct Answer is:
A
`I=int_(0)^(pi//4)(sinx+cosx)/(25-16(sinx+cosx)^(2)) dx`
Let `sinx-cosx=t`
`:.I=int_(-1)^(0)(dt)/(25-16t^(2))`
`=1/16int_(-1)^(0)(dt)/((5/4)^(2)-t^(2))`
`=1/16 . 1/2 . 5/4 log [|(5/4+t)/(5/4-t)|]_(-1)^(0)`
`=1/40[log1-"log"1/9]`
`=(log 9)/40`
`=1/20 log 3`
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CENGAGE PUBLICATION-DEFINITE INTEGRATION -SCQ_TYPE
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