Step-by-Step Guide to Calculate the Integral of Sqrt(x^2+1)?

Calculating an integration of Sqrt(x^2+1) can be a daunting task for anyone. However, it's not impossible. With the right knowledge and techniques, you can easily calculate an integration of Sqrt(x^2+1). In this article, we'll provide a step-by-step guide on how to calculate the integration of Sqrt(x^2+1).

Step-by-Step Guide

Follow these steps to calculate the integration of Sqrt(x^2+1):

1.Rewrite the integration using the basic formula:

$$\int\sqrt{\left(x^2 + 1\right) dx} = \int\left(x^2 + 1\right)^{\frac{1}{2}} dx$$

2.Apply the power rule to solve the integration:

$$\int\left(x^2 + 1\right)^{\frac{1}{2}} dx = \frac{2}{3}\left(x^2 + 1\right)^{\frac{3}{2}} + C$$

3.Use the chain rule to evaluate the integration for a given function, which yields the solution:

$$\int\sqrt{\left(x^2 + 1\right) dx} = \frac{2}{3}\left(f(x)^2 + 1\right)^{\frac{3}{2}} + C$$

Where, $C$ is a constant of integration. This is the complete solution for the calculation of integration of Sqrt(x^2 + 1).

FAQs

What is an integration?

An integration is a mathematical process to calculate the area under a curve. It allows us to solve complicated equations and can be used in calculus and calculus-based fields.

What is the Power Rule?

The Power Rule is a mathematical rule used to integrate powers of variables. It states that the integral of any power of a variable $x$ is that power plus one divided by the power plus one, multiplied by the integral of the original power of the variable $x$.

What is the Chain Rule?

The Chain Rule is a mathematical rule used to differentiate composite functions. In the context of integration, it is used to evaluate integrals involving composite functions by breaking them down into simpler integrals.

How can I solve an integration?

The best way to solve an integration is by using basic integration rules. You can then apply the Power Rule and Chain Rule to evaluate the integration. If you need more help, you can refer to online tutorials on how to solve an integration.

What is a constant of integration?

A constant of integration is a constant that is added to the result of an indefinite integral during the integration process. It is a mathematical representation of the constant function $f(x) = C$.

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