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Find :`int((3sintheta-2)costheta)/(5-cos^2theta-4sintheta)dthetathetadot`

Answer» `int((3sintheta-2)/(5-cos^2theta-4sintheta)*costheta d theta`
Let `t=sintheta`
`int((3t-2)/(5-(1-t^2)-4t)dt`
`int(3t-2)/(t^2+2^2-2t2)dt`
`int(3t-2)/(t-2)^2dt`
`int3/(t-2)^2dt+int4/(t-2)dt`
`x=t-2,dx=dt`
`int3/x^2dx+int4/xdx`
`-3/x+4log|x|+C`
`-3/(t-2)+4log(|t-2|)+c`
`-3/(sintheta-2)+4log|sintheta-2|+c`
`3/(2-sintheta)+4log(2-sintheta)+c`.


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