document.write( "Question 1115246: Evaluate the following definite integral
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\n" ); document.write( "∫ x(x² + 3)² dx where a =1 and b = 6.
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Algebra.Com's Answer #730146 by ikleyn(52794) $\"\"$ $\"About$

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document.write( "  6\r\n" );
document.write( "  ∫ x(x² + 3)² dx  = \r\n" );
document.write( "  1\r\n" );
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document.write( "     6\r\n" );
document.write( "= .∫ (x² + 3)^2*(dx²)  = \r\n" );
document.write( "     1\r\n" );
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document.write( "     6\r\n" );
document.write( "= .∫ (x² + 3)²*d(x²+3)  =   // make substitution/replacement  x²+3 ---> t;  1 --->  1^2+3 = 4;  6 ---> 6^2+3 = 39.  You will get\r\n" );
document.write( "     1\r\n" );
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document.write( "    39\r\n" );
document.write( "= .∫ t^²*dt =   // it is just an elementary integral from the tables\r\n" );
document.write( "     4\r\n" );
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document.write( "        |39\r\n" );
document.write( "= . | = . = 9875.833.\r\n" );
document.write( "        |4\r\n" );
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