Question

Integrate the functions. $$ \frac{x}{9-4 x^{2}} $$

   Integrate the functions.
$$
\frac{x}{9-4 x^{2}}
$$

NCERT Class 12 Part 2 - Math

NCERT Class 12 Part 2 - Math

Pawan K. Jain 2006 Edition

Chapter 7, Problem 15

Instant Answer

Solved by Expert Prashansha Kaushik

06/18/2021

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We can solve this integral by using the method of substitution. Show more…

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Integrate the functions. $$ \frac{x}{9-4 x^{2}} $$

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Key Concepts

U-Substitution

U-substitution is a method of changing the variable of integration to simplify the integrand. It is particularly effective when a part of the integrand and its derivative are both present, allowing the integral to be rewritten in a simpler form that is easier to evaluate.

Integration

Integration is a fundamental concept in calculus that involves finding the antiderivative or the area under the curve of a function. It is used to solve problems related to accumulation of quantities and the net change over an interval.

Rational Functions

Rational functions are expressions formed by the ratio of two polynomials. Their integration often requires specific techniques since the structure of the numerator and denominator can allow for methods such as u-substitution or partial fraction decomposition to simplify the process.

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