document.write( "Question 971772: Find an antiderivative for −7 ( −6 x−5 )^(1/8)\r
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( "

Algebra.Com's Answer #594275 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
Find an antiderivative for \"-7%28-6x-5%5E%22%22%29%5E%281%2F8%29\"
\n" ); document.write( "
\r\n" );
document.write( "Let an antiderivative be = \"k%2Au%5En\"\r\n" );
document.write( "\r\n" );
document.write( "the derivative of \"k%2Au%5En\" is \"k%2An%2Au%5E%28n-1%29expr%28%28du%29%2F%28dx%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "Therefore \"k%2An%2Au%5E%28n-1%29expr%28%28du%29%2F%28dx%29%29\"\"%22%22=%22%22\"\"-7%28-6x-5%5E%22%22%29%5E%281%2F8%29\"\r\n" );
document.write( "\r\n" );
document.write( "Set the bases equal to each other and the exponents equal to each other\r\n" );
document.write( "\r\n" );
document.write( "\"u=%28-6x-5%5E%22%22%29\" and \"n-1=1%2F8\"\r\n" );
document.write( "\r\n" );
document.write( "Take the derivative; solve for n\r\n" );
document.write( "\r\n" );
document.write( "\"%28du%29%2F%28dx%29=-6\" and \"n=1%2B1%2F8=9%2F8\"\r\n" );
document.write( "\r\n" );
document.write( "Substituting,\r\n" );
document.write( "\r\n" );
document.write( "\"k%2Aexpr%289%2F8%29%2A%28-6x-5%5E%22%22%29%5E%281%2F8%29%2A%28-6%29\"\"%22%22=%22%22\"\"-7%28-6x-5%5E%22%22%29%5E%281%2F8%29\"\r\n" );
document.write( "\r\n" );
document.write( "Multiply both sides by 8 to clear the fraction:\r\n" );
document.write( "\r\n" );
document.write( " \"k%2A9%2A%28-6x-5%5E%22%22%29%5E%281%2F8%29%2A%28-6%29\"\"%22%22=%22%22\"\"-56%28-6x-5%5E%22%22%29%5E%281%2F8%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"-54%2Ak%2A%28-6x-5%5E%22%22%29%5E%281%2F8%29\"\"%22%22=%22%22\"\"-56%28-6x-5%5E%22%22%29%5E%281%2F8%29\"\r\n" );
document.write( "\r\n" );
document.write( "Divide both sides by \"%28-6x-5%5E%22%22%29%5E%281%2F8%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"-54%2Ak\"\"%22%22=%22%22\"\"-56\"\r\n" );
document.write( "\r\n" );
document.write( "\"k\"\"%22%22=%22%22\"\"%28-56%29%2F%28-54%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"k\"\"%22%22=%22%22\"\"28%2F27\"\r\n" );
document.write( "\r\n" );
document.write( "So an antiderivative = \"k%2Au%5En\"\"%22%22=%22%22\"\"expr%2828%2F27%29%28-6x-5%5E%22%22%29%5E%289%2F8%29\"\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );