Class 12th – Integral of sec x dx | Integrals | Tutorials Point

Integral of cot x dx
Lecture By: Er. Ridhi Arora, Tutorials Point India Private Limited.

[mpniko]

But why to multiply and divide by (secx+tanx) yhi to main chiz h aise rattafication se to accha seedhe result hi yad na krlo krna hi kya h bas secx+tanx se pehle log lgana h 😂

[vishalbhatia]

Secant x can be written as 1/Cos x and then multiply both Numerator and Denominator by Cos x, so we get Cos x / cos square x = make the denominator as 1- sin square x and put u = sin x so du = cos x dx. Integrand becomes du/1 - u sqyare - its integrable !!

There are 4 ways to integrate secant x !!

[creamcheese]

The big disadvantage of this method is that multiplying top and bottom by (secx + tanx) is hardly obvious or intuitive. It just works. Better to multiply 1/cos x top and bottom by cos x to get cos x/(1-sin^2x). Let p=sin x, then integrate 1/(1-p^2) =1/(1-p)x(1+p) by partial fractions.

[AdityaSharma-gfzs]

Very simple and easy to understand tutorial. Thanks a lot !

[rakshithaparishan]

Mam why we put only secantx+tanx why we don't consider anything

[lovishdhingra]

Best YouTube channel and best teacher ever mam

[renston]

Mam I have a doubt.We can write secx as 1/cosx.Now it is in
the form of 1/x.Integral of 1/x is
Logx+c.Why can't we solve like this.Can we solve like this.Or is it wrong.Please clarify my doubt

[poripretty]

Thank you so much ma'am. It is very easy and simple to understand.thanx a lot again

[zinsinag]

Thank u so much ma'am .It was really helpful.

[captainstreamer]

Mam There is deference between ln and log " ap kahi pe kavivbi kuch vi nehi likh sakte " 1/x dx ke integration ko agar koi log bole toh uska mathematics parna hi bekar hain...

[unknownatgoogle]

Which is also equal to = log | tan(π/4 +x/2) | +C

[uttiyamajumdar]

This is not at all an acceptable method. The factor that you have used to multiply the numerator and the denominator cannot be intuitively arrived at. It is as if you know the answer already and accordingly used the factor to arrive at the answer. Instead of this method, one should proceed as follows so that no such intuitive approach will be required:
I=∫secxdx
(Let, secx=u so that secxtanx dx=du ; or, dx=du/utanx=du/(u√(u^2-1)))

=ln|secx+tanx|+C

[PIYUSHJATAP]

I think u make integration too essy 🙏🏻

[helpinghandnepra]

Ur line "It is nothing but...." irritates me😬

[vishalbhatia]

Integration of Sin x dx = - cos x + C

But the integral of Sin x can also be computed using a Trig to Trig to an Algebraic Function.

This was devised by a famous Mathematician who did not finish his Maths degree !!