Integrate sec^2(x)tan(X)dx

This can be done with integration by substitution. If we let u=tanx then du/dx=sec^2(X). If we substitute U into the integrand we get it being u(sec^2(X))dx. rearranging the du/dx equation to make dx the subject and we get dx=1/(sec^2(x)) du and so subbing this into the equation we see the sec^2(x) cancel. This leaves the integral of udu, which gives 1/2(u^2) + c, which is (1/2)tan^2(x) + c when subbing u=tan(x) back in.

AZ
Answered by Amin Z. Maths tutor

22363 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

f (x) = (x^2 + 4)(x^2 + 8x + 25). Find the roots of f (x) = 0


Differentiate the expression x^6+5x^4+3 with respect to x


If y = 2/3 x^3 + x^2; a) What is dy/dx? b) Where are the turning points? c) What are the nature of the turning points?


How do i solve differential equations?


We're here to help

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

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning