# How do you find the integral of #int 2secxtanx dx#?

2secx+C

Justification

The definition of a function's differential is:

Simple integration theory formula:

By signing up, you agree to our Terms of Service and Privacy Policy

To find the integral of ( \int 2\sec(x)\tan(x) , dx ), you can use substitution. Let ( u = \sec(x) + \tan(x) ). Then, ( du = (\sec(x)\tan(x) + \sec^2(x)) , dx ).

Notice that ( du = (\sec(x)\tan(x) + \sec^2(x)) , dx ) matches the integrand ( 2\sec(x)\tan(x) , dx ).

Thus, the integral becomes:

[ \int 2\sec(x)\tan(x) , dx = \int 2 , du = 2u + C ]

Where ( C ) is the constant of integration.

Finally, substitute back ( u = \sec(x) + \tan(x) ) to get the final answer:

[ \int 2\sec(x)\tan(x) , dx = 2(\sec(x) + \tan(x)) + C ]

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you find the integral of #sqrt(13+12x-x^2)dx#?
- How do you integrate #int e^(sec2x)sec2xtan2xdx# from #[pi/3,pi/2]#?
- How do you use the limit process to find the area of the region between the graph #y=x^2+2# and the x-axis over the interval [0,1]?
- How do you integrate #sin(x)*(e)^(2 x) dx#?
- How do you find the antiderivative of #(e^sin(t)) *(cos(t))#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7