∫x √((1+x^2)) d x

Name: Problem 9, Chapter 27: Engineering Mathematics
Uploaded: 2023-03-24T06:44:58-08:00
Duration: 1 min 35 s
Channel: Khushbu Rani
Description: ∫x √((1+x^2)) d x

step 1 Hi, there is a question and this I need to integrate this So, let us write to multiply and divid

Question

$\int x \sqrt{\left(1+x^{2}\right)} \mathrm{d} x$

   $\int x \sqrt{\left(1+x^{2}\right)} \mathrm{d} x$

Engineering Mathematics

K. A. Stroud, Dexter… 5th Edition

Chapter 27, Problem 9

Instant Answer

Solved by Expert Khushbu Rani

03/24/2023

Step 1

Step 1: First, we rewrite the integral by multiplying and dividing by 2: \[2 \int x \sqrt{\left(1+x^{2}\right)} \mathrm{d} x / 2\] Show more…

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$\int x \sqrt{\left(1+x^{2}\right)} \mathrm{d} x$

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Key Concepts

u-Substitution

This technique simplifies integration by introducing a new variable in place of a complicated expression, reducing the integral to a form that is easier to evaluate. It is especially useful when the integrand includes a function and its derivative, allowing the substitution to cancel out parts of the original expression.

Reverse Chain Rule

The reverse chain rule, often applied through u-substitution, is the process of recognizing the derivative of an inner function within a composite function. This recognition allows for the inversion of the chain rule used in differentiation, thereby simplifying the integration process.

Antiderivatives

Finding an antiderivative involves determining a function whose derivative equals the given integrand. This concept is central to integral calculus, serving as the basis for computing indefinite integrals and solving problems related to areas and accumulation functions.

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