document.write( "Question 886474: Please help. Integrate {(1-cotx)^2 \n" ); document.write( "
Algebra.Com's Answer #535925 by Edwin McCravy(20060)\"\" \"About 
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document.write( "\"int%28%281-cot%28x%29%29%5E2%2Cdx%29\"\r\n" );
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document.write( "                          Square the binomial:\r\n" );
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document.write( "\"int%28%281-2cot%28x%29%2Bcot%5E2x%29%2Cdx%29\"\r\n" );
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document.write( "                          Write as the sum of three integrals:\r\n" );
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document.write( "\"int%28%281%29%2Adx%29\"\"%22%22%2B%22%22\"\"int%28%28-2cot%28x%29%29%2Adx%29\"\"%22%22%2B%22%22\"\"int%28%28cot%5E2x%29%2Adx%29\"\r\n" );
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document.write( "                          Take out constant in second integral, and use the\r\n" );
document.write( "                          Pythagorean identity \"cot%5E2x=csc%5E2x-1\" in the third integral: \r\n" );
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document.write( "\"int%28dx%29\"\"%22%22-%22%22\"\"2%2Aint%28%28cot%28x%29%29%2Adx%29\"\"%22%22%2B%22%22\"\"int%28%28csc%5E2x-1%29%2Adx%29\"\r\n" );
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document.write( "\"int%28dx%29\"\"%22%22-%22%22\"\"2%2Aint%28%28cot%28x%29%29%2Adx%29\"\"%22%22%2B%22%22\"\"int%28%28csc%5E2x%29%2Adx%29\"\"%22%22%2B%22%22\"\"int%28%28-1%29%2Adx%29\"\r\n" );
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document.write( "\"int%28dx%29\"\"%22%22-%22%22\"\"2%2Aint%28%28cot%28x%29%29%2Adx%29\"\"%22%22%2B%22%22\"\"int%28%28csc%5E2x%29%2Adx%29\"\"%22%22-%22%22\"\"int%28dx%29\"\r\n" );
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document.write( "                          The first and last integrals cancel\r\n" );
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document.write( "\"-2%2Aint%28%28cot%28x%29%29%2Adx%29\"\"%22%22%2B%22%22\"\"int%28%28csc%5E2x%29%2Adx%29\"\r\n" );
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document.write( "                          Use the integral formulas:\r\n" );
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document.write( "                          \"int%28%28cot%28u%29%29%2Cdu%29=ln%28abs+%28sin%28u%29%29+%29%2BC\" and \"int%28%28csc%5E2u%29%2Cdu%29=-cot%28u%29%2BC\"\r\n" );
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document.write( "\"-2%2Aln%28abs+%28sin%28x%29%29+%29+%2B+%28-cot%28x%29%29%2BC\"\r\n" );
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document.write( "\"-2%2Aln%28abs+%28sin%28x%29%29+%29+-+cot%28x%29%2BC\"\r\n" );
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document.write( "Edwin
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