document.write( "Question 1198799: integrate (x ^ 2)/(x ^ 3 + 4) dx from 0 to 5 =\r
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( "

Algebra.Com's Answer #832499 by mccravyedwin(407)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "\"int%28+%28x%5E2%29%2F%28x%5E3+%2B+4%29%2C+dx%2C0%2C5%29\"\r\n" );
document.write( "\r\n" );
document.write( "Notice that the numerator has the same power of x, (2), as the derivative of\r\n" );
document.write( "the denominator \"x%5E3%2B4\" has. The derivative of the denominator is \"3x%5E2\".\r\n" );
document.write( "\r\n" );
document.write( "So the numerator can be made into the derivative of the denominator by inserting\r\n" );
document.write( "a 3 factor in the numerator and multiplying by 1/3 on the outside of the\r\n" );
document.write( "integral sign.\r\n" );
document.write( "\r\n" );
document.write( "\"expr%281%2F3%29int%28+%283x%5E2%29%2F%28x%5E3+%2B+4%29%2C+dx%2C0%2C5%29\"\r\n" );
document.write( "\r\n" );
document.write( "We use the formula \"int%28du%2Fu%29\"\"%22%22=%22%22\"\"ln%28u%29\"\"%22%22%2B%22%22\"\"C\"\r\n" );
document.write( "\r\n" );
document.write( "\"expr%281%2F3%29ln%28x%5E3%2B4%29\"\"matrix%283%2C1%2C%22%7C5%22%2C%22%7C++%22%2C%22%7C0%22%29\"\"%22%22=%22%22\"\"expr%281%2F3%29%28ln%285%5E3%2B4%29-ln%280%5E3%2B4%29%5E%22%22%29\"\"%22%22=%22%22\"\"expr%281%2F3%29%28ln%28129%29-ln%284%29%5E%22%22%29\".\r\n" );
document.write( "\r\n" );
document.write( "That is approximately 1.157839348\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );