Find the antiderivative of the function f(x)=cos(2x)+5.

In order to find the antiderivative of the function we're given, we first have to study the general structure of the function. This function consists of a sum between cos(2x) and 5. Therefore, we have : F(x)=∫cos(2x)dx+∫5dx.
We will first focus on ∫cos(2x)dx. Let's solve this by substitution. Let g(x)=2x. We have : ∫cos(g(x))g'(x)dx=∫cos(u)du=sin(u)+C. Hence, ∫cos(2x)*2dx=sin(2x)+C. Thus, ∫cos(2x)=sin(2x)/2+C.
Let's now focus on ∫5dx. This one is fairly easy as we know how to integrate constants: We have ∫5dx = 5x+C.
Therefore, F(x)=(sin(2x)/2)+5x+c

TD
Answered by Tutor149135 D. Maths tutor

4758 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Using first principles find the differential of x^2


Let p(x) = 30 x^3 -7 x^2 - 7 x + 2. Prove that (2x + 1) is a factor of p(x) and factorise p(x) completely.


The Curve C has equation y = 3x^4 - 8x^3 -3. Find the first and second derivative w.r.t x and verify that y has a stationary point when x = 2. Determine the nature of this stationary point, giving a reason for your answer.


Find the exact value of x from the equation 3^x * e^4x = e^7


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