SOLUTION: Find the indefinite integral and check the result by differentiation. (Use C for the constant of integration.) {{{int( "[csc(y)cot(y)"-"sec(y)tan(y)]", dy )}}}

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Question 287733: Find the indefinite integral and check the result by differentiation. (Use C for the constant of integration.)

int%28+%22%5Bcsc%28y%29cot%28y%29%22-%22sec%28y%29tan%28y%29%5D%22%2C+dy+%29
Answer by Edwin McCravy(20081) About Me  (Show Source):
You can put this solution on YOUR website!

If you know these four formulas, which are in all
calculus books: 

int%28%22csc%28u%29cot%28u%29%22%2Cdu%29=-csc%28u%29%2BC
int%28%22sec%28u%29tan%28u%29%22%2Cdu%29=sec%28u%29%2BC
d%2F%28dx%29sec%28u%29=%22%5Bsec%28u%29tan%28u%29%5Du%27%22
d%2F%28dx%29csc%28u%29=-%22%5Bcsc%28u%29cot%28u%29%5Du%27%22

then your problem is immediate:

int%28+%22%5Bcsc%28y%29cot%28y%29%22-%22sec%28y%29tan%28y%29%5D%22%2C+dy+%29

int%28%22csc%28y%29cot%28y%29%22%2Cdy%29-int%28%22sec%28y%29tan%28y%29%22%2Cdy+%29

-csc%28y%29-sec%28y%29%2BC

Checking, taking the derivative:

-%22%5B-csc%28y%29cot%28y%29%5D%22-%22sec%28y%29tan%28y%29%22%2B0

%22csc%28y%29cot%28y%29%22-%22sec%28y%29tan%28y%29%22

which is the function between the integral sign and the dy.

Edwin