I have a question concerning the integral of: (Secx)^2*(tanx). Now I get the correct answer using integration by parts: u = Secx; du = (Secx)(tanx)dx. This gives me the correct answer to the integral as (1/2)*(Secx)^2+C. The problem is that I can formulate the problem a second way, and get an incorrect answer, but I don't know why. The second (incorrect) way is by letting u = tanx; du = (secx)^2*dx. Then I get (1/2)(tanx)^2 + C which is wrong. But, what am I doing wrong. NOTE: I'm assuming d(tanx)/dx = (secx)^2, and d(secx)/dx = secx*tanx.

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I have a question concerning the integral of: (Secx)^2*(tanx). Now I get the correct answer using integration by parts: u = Secx; du = (Secx)(tanx)dx. This gives me the correct answer to the integral as (1/2)*(Secx)^2+C. The problem is that I can formulate the problem a second way, and get an incorrect answer, but I don't know why. The second (incorrect) way is by letting u = tanx; du = (secx)^2*dx. Then I get (1/2)(tanx)^2 + C which is wrong. But, what am I doing wrong. NOTE: I'm assuming d(tanx)/dx = (secx)^2, and d(secx)/dx = secx*tanx.

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Actually both answers are correct. Since (sec x)^2 = 1 + (tan x)^2, (1/2)*(sec x)^2 + C = (1/2)*(tan x)^2 + C + 1/2 = (1/2)*(tan x)^2 + D (D being a constant).
Thanks very much for the explanation. Didn't think of that. Much appreciated.

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