document.write( "Question 971771: Find an antiderivative for −5 ( −4 x^2−1 )^2
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Algebra.Com's Answer #594277 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
Find an antiderivative for \"-5%28-4x%5E2-1%29%5E2\"
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document.write( "\"-5%28-4x%5E2-1%29%5E2\"\"%22%22=%22%22\"\"-5%2816x%5E4%2B8x%5E2%2B1%29\"\"%22%22=%22%22\"\"-80x%5E4-40x%5E2-5\"\r\n" );
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document.write( "Since that has 3 terms, \r\n" );
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document.write( "Let an antiderivative be = \"a%2Ax%5En%2Bbx%5Em%2Bcx%5Ep\"\r\n" );
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document.write( "the derivative of \"a%2Ax%5En%2Bbx%5Em%2Bcx%5Ep\" is \"a%2An%2Ax%5E%28n-1%29%2Bb%2Am%2Ax%5E%28m-1%29%2Bc%2Ap%2Ax%5E%28p-1%29\"\r\n" );
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document.write( "Therefore \"a%2An%2Ax%5E%28n-1%29%2Bb%2Am%2Ax%5E%28m-1%29%2Bc%2Ap%2Ax%5E%28p-1%29\"\"%22%22=%22%22\"\"-80x%5E4-40x%5E2-5\"\r\n" );
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document.write( "Write the 5 as \"5%2Ax%5E0\"\r\n" );
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document.write( "\"a%2An%2Ax%5E%28n-1%29%2Bb%2Am%2Ax%5E%28m-1%29%2Bc%2Ap%2Ax%5E%28p-1%29\"\"%22%22=%22%22\"\"-80x%5E4-40x%5E2-5x%5E0\"\r\n" );
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document.write( "Set the corresponding exponents equal to each other\r\n" );
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document.write( "\"n-1=4\", \"m-1=2\", \"p-1=0\"\r\n" );
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document.write( "Solve for the exponents:\r\n" );
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document.write( "\"n=5\", \"m=3\", \"p=1\"\r\n" );
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document.write( "Substituting,\r\n" );
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document.write( "\"a%2A5%2Ax%5E4%2Bb%2A3%2Ax%5E2%2Bc%2A1%2Ax%5E0\"\"%22%22=%22%22\"\"-80x%5E4-40x%5E2-5x%5E0\"\r\n" );
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document.write( "\"5ax%5E4%2B3bx%5E2%2Bcx%5E0\"\"%22%22=%22%22\"\"-80x%5E4-40x%5E2-5x%5E0\"\r\n" );
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document.write( "Set the coefficients of like powers of x equal to each other\r\n" );
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document.write( "\"5a=-80\", \"3b=-40\", \"c=-5\"\r\n" );
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document.write( "\"a=-16\", \"b=-40%2F3\", \"c=-5\"\r\n" );
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document.write( "Substituting those and \"n=5\", \"m=3\", \"p=1\"\r\n" );
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document.write( "So an antiderivative = \"a%2Ax%5En%2Bbx%5Em%2Bcx%5Ep\"\"%22%22=%22%22\"\"-16x%5E5-expr%2840%2F3%29x%5E3-5x%5E1\"\r\n" );
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document.write( "Answer:  \"-16x%5E5-expr%2840%2F3%29x%5E3-5x\"\r\n" );
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document.write( "Edwin
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