# How do you find the antiderivative of #int sec^2xtanx dx#?

Method 1

by the chain rule

Method 2

by the chain rule

the 2 results can be shown to be equivalent by use of

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

To find the antiderivative of ( \int \sec^2(x) \tan(x) , dx ), you can use substitution.

Let ( u = \sec(x) ), then ( du = \sec(x) \tan(x) , dx ).

This means the integral becomes:

[ \int u^2 , du ]

[ = \frac{u^3}{3} + C ]

Now, substitute back ( u = \sec(x) ) to get the final result:

[ \frac{\sec^3(x)}{3} + 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 integrate #int x^3*sqrt(4+x^2) # using integration by parts?
- How do you evaluate #int dx/(x^2+4x+13)# from #[-2, 2]#?
- How do you find the integral #ln(x^2+x+1)#?
- How do you integrate #int (2x+1)/(4x^2+12x-7) dx# using partial fractions?
- How do you integrate # (x^2+8)/(x^2-5x+6)# using partial fractions?

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