step 1 Hey, so we need to evaluate the indefinite integrals. So we have a question that is DX in the nu

Question

$\int \frac{d x}{4+x^{2}}$

Name: Problem 29, Chapter 6: The Chemistry Maths Book
Uploaded: 2021-12-29T21:42:11-08:00
Duration: 1 min
Channel: John Nicolle
Description: ∫(d x)/(4+x^2)

   $\int \frac{d x}{4+x^{2}}$

The Chemistry Maths Book

Erich Steiner 2nd Edition

Chapter 6, Problem 29

Instant Answer

Solved by Expert John Nicolle

12/29/2021

Step 1

Step 1: First, we can rewrite the integral as follows: \[\int \frac{d x}{4+x^{2}} = \frac{1}{2} \int \frac{2 dx}{4+x^{2}}\] Show more…

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$\int \frac{d x}{4+x^{2}}$

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Key Concepts

Standard Integral Formula for 1/(a²+x²)

A well-known result in integration is the formula ? dx/(a²+x²) = (1/a) arctan(x/a) + C. This formula simplifies the evaluation of integrals involving quadratic expressions in the denominator by directly relating them to the inverse tangent function.

Indefinite Integral

An indefinite integral represents the family of antiderivatives of a function. When evaluating an indefinite integral, the result includes an arbitrary constant because differentiation of a constant results in zero, thus representing all functions whose derivative yields the original integrand.

Inverse Trigonometric Functions

Inverse trigonometric functions, such as arctan, arise in integration when dealing with expressions that match specific patterns. The arctan function is particularly common when integrating functions of the form 1/(a²+x²), linking algebraic expressions to trigonometric identities.

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