... Good day Newton, I have just one tiny comment at time 8:48: Why the u^2 + u in the denominator of the integrand instead of u^2 + 1? ... I know it is accidentally written ... Great presentation from your hand as always; I like these integrals full of surprises ... Take care, Jan-W
Learning from you. I would suggest others to try solving the question by simplifying firstly the expression using the identity (sin^2+cos^2=1 --> sin^2 = 1-cos^2). I think this will save time.
Hi, it's a magical task, the derivation of the first part is great. If we multiply by 1/(cosx)^2, we get (1/2) int (secx^2/(tanx^2+2))dx, and let t=tanx, (1/2)int (1/( t^2+2))dt and we can already write I=(1/(2sqrt2))*arctan(tanx/sqrt2) + C, Thank's
@@PrimeNewtons Thank's Prime Newtons, her presentations are exciting, understandable, we can supplement our knowledge ... The written t=tanx helped with the solution!
![Integrating using t=tan(x/2) substitution - [The Weierstrass substitution]](/img/1.gif)
... Good day Newton, I have just one tiny comment at time 8:48: Why the u^2 + u in the denominator of the integrand instead of u^2 + 1? ... I know it is accidentally written ... Great presentation from your hand as always; I like these integrals full of surprises ... Take care, Jan-W
Oops! I noticed after uploading. I will pin your comment. Thank you, Jan-W.
Wow!!!!!, i had no idea to attempt this integral, thanks mr prime newtons, more blessings
Learning from you. I would suggest others to try solving the question by simplifying firstly the expression using the identity (sin^2+cos^2=1 --> sin^2 = 1-cos^2). I think this will save time.
ur explaination is the best ever i thank u for everything u do
thank u for ur help ❤❤
Hi, it's a magical task, the derivation of the first part is great. If we multiply by 1/(cosx)^2, we get (1/2) int (secx^2/(tanx^2+2))dx, and let t=tanx, (1/2)int (1/( t^2+2))dt and we can already write I=(1/(2sqrt2))*arctan(tanx/sqrt2) + C, Thank's
That's cool!
@@PrimeNewtons Thank's Prime Newtons, her presentations are exciting, understandable, we can supplement our knowledge ... The written t=tanx helped with the solution!
it was good the way you made things look easy but always start by showing us the reason why we choose to use that method of intergration
It is tricky but you are explaining it very very good
Thank you sir, but I have a question at 8:08
why is it sqrt2 and not 2
its arctan derivative we need 1 / 1 + u^2 so we take the sqrt of 2 to obtain this form
❤❤❤❤❤
👍
This is Great..😅
In minute 8:47 your wrote u instead of 1 in the denominator
Here for your cap[hat]
that triangle is realy good way to get sin and cos my doctor didnt use that
what if i have in denominator tan or cot ?
Boses