document.write( "Question 287733: Find the indefinite integral and check the result by differentiation. (Use C for the constant of integration.)
\n" ); document.write( "
\n" ); document.write( "\"int%28+%22%5Bcsc%28y%29cot%28y%29%22-%22sec%28y%29tan%28y%29%5D%22%2C+dy+%29\" \n" ); document.write( "
Algebra.Com's Answer #208531 by Edwin McCravy(20081)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "If you know these four formulas, which are in all\r\n" );
document.write( "calculus books: \r\n" );
document.write( "\r\n" );
document.write( "\"int%28%22csc%28u%29cot%28u%29%22%2Cdu%29=-csc%28u%29%2BC\"\r\n" );
document.write( "\"int%28%22sec%28u%29tan%28u%29%22%2Cdu%29=sec%28u%29%2BC\"\r\n" );
document.write( "\"d%2F%28dx%29\"\"sec%28u%29=%22%5Bsec%28u%29tan%28u%29%5Du%27%22\"\r\n" );
document.write( "\"d%2F%28dx%29\"\"csc%28u%29=-%22%5Bcsc%28u%29cot%28u%29%5Du%27%22\"\r\n" );
document.write( "\r\n" );
document.write( "then your problem is immediate:\r\n" );
document.write( "\r\n" );
document.write( "\"int%28+%22%5Bcsc%28y%29cot%28y%29%22-%22sec%28y%29tan%28y%29%5D%22%2C+dy+%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"int%28%22csc%28y%29cot%28y%29%22%2Cdy%29-int%28%22sec%28y%29tan%28y%29%22%2Cdy+%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"-csc%28y%29-sec%28y%29%2BC\"\r\n" );
document.write( "\r\n" );
document.write( "Checking, taking the derivative:\r\n" );
document.write( "\r\n" );
document.write( "\"-%22%5B-csc%28y%29cot%28y%29%5D%22-%22sec%28y%29tan%28y%29%22%2B0\"\r\n" );
document.write( "\r\n" );
document.write( "\"%22csc%28y%29cot%28y%29%22-%22sec%28y%29tan%28y%29%22\"\r\n" );
document.write( "\r\n" );
document.write( "which is the function between the integral sign and the \"dy\".\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );