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.

Answered by Amin Z. Maths tutor

19981 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Differentiate the function f(x) = sin(x)/(x^2 +1) , giving your answer in the form of a single fraction. Is x=0 a stationary point of this curve?


Question 6 from Aqa 2017 June paper for C4, the vector question


Determine the tangent to the curve y = sin^2(x)/x at the point, x = pi/2. Leave your answer in the form ax+by+c=0


Find R and a such that 7*cos(x)+3*sin(x)=Rcos(x-a)


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences