# How do you evaluate the integral #int sec^3x/tanx#?

Enjoy Maths.!

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

To evaluate the integral (\int \frac{\sec^3(x)}{\tan(x)} , dx), you can use trigonometric substitution. Let (u = \tan(x)), then (du = \sec^2(x) , dx). This substitution transforms the integral into a simpler form, leading to:

[ \int \frac{\sec^3(x)}{\tan(x)} , dx = \int \frac{1}{u^3} , du ]

Now, integrate (\frac{1}{u^3}) with respect to (u), and then substitute back (u = \tan(x)) to obtain the final result.

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.

- If # int_0^3 f(x) dx = 8 # then calculate? (A) (i) #int_0^3 2f(x) dx#, (ii) #int_0^3 f(x) + 2 dx# (B) #c# and #d# so that #int_c^d f(x-2) dx #
- How do you find the area under the graph of #f(x)=e^(-2lnx)# on the interval [1, 2]?
- How do you find the antiderivative of #f(x)=(x^3-2x^2+x)/x#?
- What is the integral of #int cos^3 (x)dx# from 0 to pi/2?
- How do you integrate #(x^2 + 2x -5) / [(x - 2)*(x+1)*(x^2+1)]#?

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