# integrate by parts $\int x e^{\sec^2 x}\ (1+\tan^2x) \, dx$.

i want to integrate $$\int x e^{\sec^2 x}\ (1+\tan^2x)\,dx.$$ I've tried using integration by parts and doesnt get the results. im stuck. anybody can help me ? thankyou.

• It should be \sec to get it right, actually \sec^2 . Next, I am guessing that the thing you have typed as tg^2 x is actually tangent squared, in which case it should be \tan^2 x – Will Jagy Jun 4 '18 at 2:37
• Worth remembering that $\frac{d}{dx}\tan(x) = \sec^2(x)$ – Kaynex Jun 4 '18 at 2:39
• I have tried and the result will appear integration by part on one side continuously. – bhidara Jun 4 '18 at 2:46
• What is $tg^2x$? EDIT: Ah I see now. Keep in mind that $1+\tan^2x$ is the same as $\sec^2x$ – Badr B Jun 4 '18 at 2:53
• yah, tg is tan. thankyou for you correction. – bhidara Jun 4 '18 at 3:34