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