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Evaluate: int1/(4sin^2x+4sinxcosx+5cos^2...

Evaluate: `int1/(4sin^2x+4sinxcosx+5cos^2x)\ dx`

Text Solution

Verified by Experts

I=`int1/(4sin^2x+4sinxcosx+5cos^2x)\ dx`
`I=∫(dtanx)/((4tan^2x+4tanx+1)+4)`​
`I=∫(dtanx)/((2tanx+1)^2+4)​`
`I=1/8​tan^(−1)(2tanx+1​)/2+c`
`I=1/8​tan^(−1)(tanx+1/2​)+c`
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Knowledge Check

  • If int(1)/(4sin^(2)x+4sin x cos x+5cos^(2)x)dx=A tan^(-1)(B tanx+C)+k , then

    A
    `A=1//4, B=1//2, C=1`
    B
    `A=1//2, B=1//4,C=1`
    C
    `A=1, B=1//2, C=1//4`
    D
    `A=1//4, B=1, C=1//2`

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