MI
Answered byMolly I.Maths Tutor

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

Related Maths A Level answers

All answers ▸

differentiate with respect to x: (x^3)(e^x)


A general function f(x) has the property f(-x)=-f(x). State a trigonometric function with this property and explain using the Maclaurin series expansion for this function why this property holds. Write down the integral in the limits -q to q of f(x) wrt x


How do you sketch the curve y=(x^2 - 4)(x+3), marking on turning points and values at which it crosses the x axis


A circle C with centre at the point (2, –1) passes through the point A at (4, –5). Find an equation for the circle C.


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences