Question

How to integrate this using substitution? http://puu.sh/1TzKT

Answer 1

Let \(u=1-\tan x\), i.e. \(du=-\sec^2x\ dx\). We can rewrite our integral as follows:$$\int\left(\frac{\sec x}{u}\right)^2dx=\int\frac{\sec^2x}{u^2}dx=-\int\frac1{u^2}du$$

Answer 2

Thanks and you look like a genius/professional hacker/code breaker

Answer 3

For problems like these it's a good idea to look to the denominator for our substitution and see if we can eliminate our numerator. Also, thanks I suppose (assuming that's a compliment :-p)

Answer 4

ok :D