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Evaluate the integral. 15x² dx (x + 1)(x² + 1) J = | + C

Evaluate the integral. 15x² dx (x + 1)(x² + 1) J = | + C

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Evaluate the Integral** \[ \int \frac{15x^2 \, dx}{(x+1)(x^2+1)} = \, \_\_\_\_ + C \] In this problem, we are tasked with evaluating the integral of the function \( \frac{15x^2}{(x+1)(x^2+1)} \) with respect to \( x \). The answer should be expressed in terms of \( C \), which represents the constant of integration. The integration involves breaking down the rational expression using strategies such as partial fraction decomposition to simplify the calculation.
Transcribed Image Text:**Evaluate the Integral** \[ \int \frac{15x^2 \, dx}{(x+1)(x^2+1)} = \, \_\_\_\_ + C \] In this problem, we are tasked with evaluating the integral of the function \( \frac{15x^2}{(x+1)(x^2+1)} \) with respect to \( x \). The answer should be expressed in terms of \( C \), which represents the constant of integration. The integration involves breaking down the rational expression using strategies such as partial fraction decomposition to simplify the calculation.
Expert Solution
Step 1

Here we use the partial fraction of the integrand to find the integration

∫1xdx=ln(x), ∫1x2+1dx=tan-1(x)

see below the process and calculation

 

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