document.write( "Question 985388: ∫(7x+8)/(2x^2+11x+5) dx integral by partial fraction
\n" ); document.write( "
\n" ); document.write( "

Algebra.Com's Answer #606208 by Edwin McCravy(20062)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "Rather than do your problem for you, I will instead do one \r\n" );
document.write( "EXACTLY like yours, step by step.  Instead of yours I will \r\n" );
document.write( "do this one:\r\n" );
document.write( "\r\n" );
document.write( "\"int%28%285x%2B7%29%2F%283x%5E2%2B11x-4%29%2Cdx%29\"\r\n" );
document.write( "\r\n" );
document.write( "We factor the denominator and set up for partial fractions:\r\n" );
document.write( "\r\n" );
document.write( "\"%285x%2B7%29%2F%28%283x-1%29%28x%2B4%29%29\"\"%22%22=%22%22\"}\"A%2F%283x-1%29%2BB%2F%28x%2B4%29\"\r\n" );
document.write( "\r\n" );
document.write( "Clear fractions:\r\n" );
document.write( "\r\n" );
document.write( "\"5x%2B7\"\"%22%22=%22%22\"\"A%28x%2B4%29%2BB%283x-1%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"5x%2B7\"\"%22%22=%22%22\"\"Ax%2B4A%2B3Bx-B\"\r\n" );
document.write( "\r\n" );
document.write( "Equate the coefficients of x:\r\n" );
document.write( "\r\n" );
document.write( "\"5\"\"%22%22=%22%22\"\"A%2B3B\"\r\n" );
document.write( "\r\n" );
document.write( "Equate the constant terms\r\n" );
document.write( "\r\n" );
document.write( "\"7\"\"%22%22=%22%22\"\"4A-B\"\r\n" );
document.write( "\r\n" );
document.write( "Solve the system of equations by substitution:\r\n" );
document.write( "\r\n" );
document.write( "\"system%28A%2B3B=5%2C4A-B=7%29\"\r\n" );
document.write( "\r\n" );
document.write( "A=5-3B,       4A-B=7\r\n" );
document.write( "         4(5-3B)-B=7 \r\n" );
document.write( "          20-12B-B=7\r\n" );
document.write( "            20-13B=7\r\n" );
document.write( "              -13B=-13\r\n" );
document.write( "                 B=1\r\n" );
document.write( "\r\n" );
document.write( "A=5-3(1)\r\n" );
document.write( "A=5-3\r\n" );
document.write( "A=2\r\n" );
document.write( "\r\n" );
document.write( "\"%285x%2B7%29%2F%28%283x-1%29%28x%2B4%29%29\"\"%22%22=%22%22\"}\"2%2F%283x-1%29%2B1%2F%28x%2B4%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"int%28%285x%2B7%29%2F%283x%5E2%2B11x-3%29%2Cdx%29\"\"%22%22=%22%22\"\r\n" );
document.write( "\r\n" );
document.write( "\"int%28%282%2F%283x-1%29%2B1%2F%28x%2B4%29%29%2Cdx%29\"\"%22%22=%22%22\"\"int%28%282%2F%283x-1%29%29%2Cdx%29\"\"%22%22%2B%22%22\"\"int%28%281%2F%28x%2B4%29%29%2Cdx%29\"\"%22%22=%22%22\"\r\n" );
document.write( "\r\n" );
document.write( "\"2int%28%281%2F%283x-1%29%29%2Cdx%29\"\"%22%22%2B%22%22\"\"ln%28x%2B4%29\"\"%22%22%2B%22%22\"\"C\"\"%22%22=%22%22\"\r\n" );
document.write( "\r\n" );
document.write( "\"expr%282%2F3%29int%28%283%2F%283x-1%29%29%2Cdx%29\"\"%22%22%2B%22%22\"\"ln%28x%2B4%29\"\"%22%22%2B%22%22\"\"C\"\"%22%22=%22%22\" \"expr%282%2F3%29ln%283x-1%29\"\"%22%22%2B%22%22\"\"ln%28x%2B4%29\"\"%22%22%2B%22%22\"\"C\"\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );