document.write( "Question 1208301: Hi can you help please:
\n" ); document.write( "int (3 x^3) (sqrt(16-x^2)) dx
\n" ); document.write( "Just not sure if my trig substitutions are working \n" ); document.write( "
Algebra.Com's Answer #846632 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"int%28%283x%5E3%29+%28sqrt%2816-x%5E2%29%29%2Cdx%29\"\r\n" );
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document.write( "That x3 factor is going to make trig substitution difficult.\r\n" );
document.write( "So let's not try trig substitution, but try algebraic substitution instead.\r\n" );
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document.write( "\"u=16-x%5E2\" => \"x%5E2=16-u\"\r\n" );
document.write( "\"du=-2x%2Adx\"\r\n" );
document.write( "\"dx=-du%2F%282x%29\"\r\n" );
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document.write( "\"int%28%283x%5E3%29+%28sqrt%28u%29%29%28-du%2F%282x%29%29%29\"\r\n" );
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document.write( "\"expr%28-3%2F2%29int%28%28x%5E2%29+%28sqrt%28u%29%29du%29%29\"\r\n" );
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document.write( "\"expr%28-3%2F2%29int%28%2816-u%29+%28sqrt%28u%29%29du%29%29%29\"\r\n" );
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document.write( "\"expr%28-3%2F2%29int%28%2816-u%29+%28sqrt%28u%29%29du%29%29\"\r\n" );
document.write( "\"expr%28-3%2F2%29int%28%2816-u%29+%28u%5E%28%221%2F2%22%29du%29%29\"\r\n" );
document.write( "\"expr%28-3%2F2%29int%28%2816u%5E%28%221%2F2%22%29-u%5E%28%223%2F2%22%29%29du%29\"\r\n" );
document.write( "\"expr%28-3%2F2%29%28int%28%2816u%5E%28%221%2F2%22%29-u%5E%28%223%2F2%22%29%29du%29%29\"\r\n" );
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document.write( "\"-16u%5E%28%223%2F2%22%29%2Bexpr%283%2F5%29u%5E%28%225%2F2%22%29%2BC\"\r\n" );
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document.write( "Your teacher may let you leave it like that, since the\r\n" );
document.write( "calculus part is over, and the rest is algebra. But\r\n" );
document.write( "here's the remaining algebra part:\r\n" );
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document.write( "factor out \"expr%281%2F5%29%2816-x%5E2%29%5E%28%223%2F2%22%29\"\r\n" );
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document.write( "\"expr%281%2F5%29%2816-x%5E2%29%5E%28%223%2F2%22%29%28-80%2B3%2816-x%5E2%29%5E%22%22%29%2BC\"\r\n" );
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document.write( "\"expr%281%2F5%29%2816-x%5E2%29%5E%28%223%2F2%22%29%28-80%2B48-3x%5E2%29%5E%22%22%2BC\"\r\n" );
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document.write( "\"expr%281%2F5%29%2816-x%5E2%29%5E%28%223%2F2%22%29%28-32-3x%5E2%29%5E%22%22%2BC\"\r\n" );
document.write( "\r\n" );
document.write( "\"expr%28-1%2F5%29%2816-x%5E2%29%5E%28%223%2F2%22%29%2832%2B3x%5E2%29%5E%22%22%2BC\"\r\n" );
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document.write( "Edwin
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