Bohrok said:For this one, you'll want to use a trig substitution instead of a regular u-substitution.
An indefinite integral is a mathematical concept that represents the antiderivative of a function. It is denoted by an integral sign (∫) followed by the function to be integrated and a variable of integration. It is used to find the general form of a function rather than a specific value.
To solve an indefinite integral, you need to use integration techniques such as substitution, integration by parts, or trigonometric substitution. First, you need to identify the function to be integrated and the variable of integration. Then, you can use the appropriate integration technique to solve the integral.
The function in the given indefinite integral is 1/(x(sqrt(x^2 - 4))). It is a rational function with a square root in the denominator. This type of function can be solved using the substitution method where you substitute a new variable for the square root and then use the chain rule to solve the integral.
The variable of integration in the given indefinite integral is x. This means that the function is being integrated with respect to x. This is important to note because it affects the limits of integration and the final result of the integral.
Indefinite integrals have various applications in mathematics, physics, and engineering. They are used to calculate displacement, velocity, and acceleration in physics. They are also used in finding the area under a curve, calculating work and energy, and solving differential equations.