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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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