Try factoring the quadratic under the root sign first. You should be able to find two linear factors.OmniNewton said:Homework Statement
Calculate the following integral:
Homework Equations
N/A
The Attempt at a Solution
from this point I tried a u-substitution by letting u = -3 + 4/x -1/x^2 but this seemed to fail.
Are any suggestions possible?
Alright thank you will attempt that now.SteamKing said:
Alright I have the indefinite integral factored for the argument however I am unsure how to proceed.OmniNewton said:
OmniNewton said:Alright I have the indefinite integral factored for the argument however I am unsure how to proceed.
I'm going to let u = x-1 which means x = u + 1 and for the second factor (3x-1) = (3x - 1 - 2 + 2) = [3(x-1) + 2]
An antiderivative, also known as an indefinite integral, is the reverse process of taking a derivative. It is a function that, when differentiated, gives the original function.
To calculate an antiderivative, you can use the power rule, product rule, quotient rule, and chain rule. You can also use integration techniques such as substitution, integration by parts, and partial fractions.
A definite integral has specific limits of integration, while an indefinite integral does not. A definite integral gives a numerical value, whereas an indefinite integral gives a function.
No, not all functions have an antiderivative. For a function to have an antiderivative, it must be continuous and differentiable on its entire domain.
Calculating an antiderivative can be useful in finding the area under a curve, determining the velocity and acceleration of an object, and solving differential equations in science and engineering applications.