MYTUTOR SUBJECT ANSWERS

1030 views

Show that the integral of tan(x) is ln|sec(x)| + C where C is a constant.

First, recall that tan(x) can be rewritten in terms of sine and cosine.

tan(x) = sin(x)/cos(x)

The rephrasing of our question suggests that we should try the substitution rule of integration.

We should substitute u=cos(x), since then du = -sin(x) dx and so sin(x) dx = -du

So the integral of tan(x) = the integral of sin(x)/cos(x) = the integral of -1/u = - ln|u| +C = - ln|cosx| +C

Now, - ln|cos(x)| = ln(|cos(x)|-1) = ln(1/|cos(x)|) = ln|sec(x)|

Therefore, the integral of tan(x) is ln|sec(x)| + C

Anja S. A Level Maths tutor, GCSE Maths tutor

2 years ago

Answered by Anja, an A Level Maths tutor with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

437 SUBJECT SPECIALISTS

£22 /hr

Bea A.

Degree: MMath Pure Mathematics (Masters) - St. Andrews University

Subjects offered:Maths, English Literature

Maths
English Literature

“I am an experienced mathematician with a personal approach to tutoring. I'm here to help you further your mathematical potential.”

£20 /hr

Kamil F.

Degree: Mechanical Engineering (Masters) - Manchester University

Subjects offered:Maths, Physics+ 2 more

Maths
Physics
Further Mathematics
.PAT.

“"It is the supreme art of the teacher to awaken joy in creative expression and knowledge." Albert Einstein”

£20 /hr

Michael E.

Degree: Chemical Engineering (Integrated Masters) - Imperial College London University

Subjects offered:Maths, Spanish+ 2 more

Maths
Spanish
Physics
Chemistry

“Imperial College London graduate with a fun and laid-back personality who will strive to help students help themselves to reach their full potential.”

MyTutor guarantee

About the author

Anja S.

Currently unavailable: until 10/09/2015

Degree: Mathematics (Masters) - Edinburgh University

Subjects offered:Maths

Maths

“Hi! My name is Anja and I am a currently in my third year of my Mmath (Masters of Mathematics) degree at the University of Edinburgh.   Previous Experience/Motivation I have previously tutored at a local Kumon centre in my hometown ...”

MyTutor guarantee

You may also like...

Other A Level Maths questions

How do you find the integral of 'x sin(2x) dx'?

Show that the cubic function f(x) = x^3 - 7x - 6 has a root x = -1 and hence factorise it fully.

How do you integrate e^x cos x

Differentiate the following: 3/2 x^(3/4) + 1/3 x^(-1/4)

View A Level Maths tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok